(CNN) -- Manchester United claimed their first points of the season with an edgy win over Fulham, whilst Chelsea continued their strong start with victory over Newcastle.
Elsewhere, Swansea continue to surprise, recording a 3-0 win over West Ham in their first home game, while Everton showed their opening win over Manchester United wasn't luck, as they conclusively beat Aston Villa 3-1.
In his team's first game at Old Trafford, Sir Alex Ferguson made it clear the performance at Everton hadn't been good enough as Wayne Rooney and Paul Scholes were dropped to the bench, with winger Nani not even in the squad.
However, the home crowd couldn't have witnessed a worse start as Fulham took the leak in the third minute. Damien Duff hushed the raucous crowd with a goal from a well worked free kick, after stand in center back Michael Carrick fouled Mladen Petric.
The fervent atmosphere had been building since it was anounced before the game that United's major summer signing, Robin Van Persie, was making his first start for the reds. The former Arsenal man didn't take long to show why his new fans were so excited by his signing, as he equalized with an exquisite finish eight minutes after United fell behind.
Once level, United worked through the gears and soon opened up a 3-1 lead. First, Shinji Kagawa, making his home debut following his move from Borussia Dortmund, poked home from close range after Tom Cleverley had a powerful shot saved. Then right back Rafael prodded home a nice cross from Ashley Young to extend United's lead.
Fulham rallied in the second half, and set the stage for an exciting finish when Nemanja Vidic headed past his own keeper to put Fulham within sight of an impressive draw.
Wayne Rooney and Danny Welbeck were introduced to try and help United take control of the game, but Fulham continued to keep the ball well. In the final minutes, Rooney suffered a nasty looking injury, which could see him out for around a month.
The striker charged down a shot from Hugo Rodallega, but the Fulham striker caught Rooney's thigh with his studs to leave a large gash in Rooney's leg.
"We made a terrible mistake for the second goal and it became a match," Ferguson told the club's tv channel after his team's 3-2 win.
"It should never have been a match, some of our football was fantastic. But we lost that second goal when we should have been in easy street."
"The first half performance was fantastic. The intensity of our game was terrific. It was a fantastic goal by Robin van Persie and by half time we were leading 3-1, it could have been four or five."
On Rooney, Ferguson confirmed: "He's gone to hospital. Obviously it looks as if he'll be out for maybe four weeks."
Fulham defender Matthew Briggs said the side was "gutted" to leave Old Trafford with nothing, and described United's goals as "sloppy."
"We're a strong minded team and obviously while we didn't play too well in the first half, we came out much stronger in the second period," Briggs told the club website.
"We've got a lot of quality in our team and we know we're capable of scoring goals. Maybe there could have been an improvement in our finishing today but you can't fault our attitude."
In the Premier League's late kick off, Chelsea enjoyed an impressive win over last season's surprise side Newcastle. The European champions were without captain John Terry, but another fantastic performance from summer signing Eden Hazard ensured Chelsea made it three wins from three games to top the table.
Newcastle's Vurnon Anita, in his first start for the club, flattened Fernando Torres in the box after 22 minutes, and Hazard stepped up to dispatch the penalty past Tim Krul.
On the stroke of half time Fernando Torres added the second when he latched on to a back heel from the young Belgian and rifled the ball past the Newcastle goalkeeper.
After their impressive opening day thrashing of QPR, the pressure was on Swansea to see if they could their form in their first home game of the season against West Ham.
The Hammers may not have provided the toughest of challenges, but Michael Laudrup's team showed his brand of fluid, attacking football will threaten opposition defences this season.
Angel Rangel opened the scoring after a mistake by Hammers goalkeeper Jussi Jaaskelainen, before new signing Michu added to his two opening day goals after a poor back pass from James Collins.
West Ham made changes at half time, but just as they were enjoying a spell of pressure Danny Graham connected with a clever cross from Wayne Routledge to add a third for the Welsh side.
"If we have the ball then the opposition can't cause us any problems," Laudrup told the Swansea website.
"We scored two goals from three or four chances, but we gave the ball away too much in the first half and that led to too many free kicks around the box.
"But in the second period we completely controlled the game and when the third goal went in, it was all over."
West Ham manager wasn't too impressed by his side's showing in South Wales.
"We were punished severely for two mistakes," he told the Swansea website.
"Jussi (Jaaskelainen) and James (Collins) are two of my most experienced players, particularly at this level, and they have unfortunately cost us the game today.
"We couldn't overcome that and Swansea ran out comfortable winners in the end.
"Up until the first goal they haven't caused us any problems. But we gifted them goals and they capitalised on the mistakes.
"As well as that, we couldn't convert the chances we did have - and that's also a bit of a concern for us."
After Everton's dominant win over Manchester United on Monday, hopes were high that David Moyes' side might avoid their infamous poor start to the season.
The Merseyside team ran out comfortable winners at Villa Park, with the home side looking well below par. Steven Pienaar opened the scoring, before Monday's hero Marouane Fallaini doubled the lead.
Croatian Nikica Jelavic added the third before half time to all but confirm the points.
In the second half, Villa center back Ciaran Clark was sent off for hauling down Jelavic as the striker, before Moroccan midfielder Karim El Ahmadi picked up a consolation for Villa.
"I am not surprised because I think we have a good team," declared Everton coach David Moyes to the Everton website.
"Can we keep them all fit? Can we play as well as we did today? Those are the questions, but when we do we are a match for most teams.
"We now have to make that performance go more than 10 games. We need to make it go 30 games. It won't always be right and we won't always win but we have to try and make that happen."
Aston Villa manager Paul Lambert was taking charge of the side at Villa Park for the first time, and conceded that the result was 'disappointing'.
"I was really disappointed. You can't, in any game of football, give someone a couple of goals start, particularly a team like Everton. You can't do it," he told Villa's official website.
"The only pleasing thing was the second half. We kept going which was pleasing but the horse has bolted."
Another manager making his home debut was Andre Villas-Boas, who was denied his first win as Tottenham boss by an impressive display y West Bromwich Albion.
WBA had enjoyed an impressive win over Liverpool last weekend, but confidence was high amongst the White Hart Lane faithful that Tottenham would recover from their loss at Newcastle last week.
There was only 15 minutes left to play when defender Benoit Assou-Ekotto rifled a 25 yard shot into the West Brom net after a game that seen dominant spells for both sides.
However, in the final minute of play, James Morrison finished off a nice move from West Brom to ensure the Midlands side continued their impressive start to the Premier League season.
"It would've been travesty if we'd lost," said Albion manager Steve Clark.
""You see them go a goal down with 16 minutes to g,o and it's a difficult place to go 1-0 down because you know the game will open up and Tottenham have got great pace on the counter attack.
"But we kept going, showed great belief and created chances."
Southampton were playing their first top flight game for seven years, but couldn't prevent Wigan taking all three points in a 2-0 win.
Franco Di Santo made up for a poor first half when he perfectly timed his run to meet a clever ball from Shaun Maloney and score his first goal of the season in the 51st minute.
Southampton managed to show some of the form that carried them to promotion last year, but couldn't find an equalizer before Wigan doubled their lead in the 80th minute.
New signing Arouna Kone stole the ball from Jose Fonte on the halfway line and raced towards the home side's goal, and simply shot past goalkeeper Kelvin Davis.
"We allowed Wigan far too much possession of the football and let them pass the ball about," suggested Southampton manager Nigel Adkins to the club's website.
"We have to give ourselves an opportunity to go and score goals, but we ended up chasing it a little bit too much,"
"This was a game we were looking to win so everyone came with an expectation, but this underlines just what a challenging division the Barclays Premier League is,"
"The momentum and enthusiasm in promoted sides is so difficult to face and in the first half hour we saw exactly that as Southampton go the ball forward and put the defence under pressure," said Wigan manager Roberto Martinez.
"Slowly we imposed ourselves on the game scored two fantastic goals and kept a clean sheet which is important in so many ways at this early stage of the season.
"Then concentration and communication has to be there and then to produce two finishes of such quality rounded off a superb effort," he told the Wigan website.
Norwich and QPR faced off at Carrow Road in a tight encounter, which was to be expected after both sides suffered miserable 5-0 defeats on the opening weekend of the season.
Simeon Jackson put the home side ahead in the 11th minute, giving new Norwich manager Chris Hughton to celebrate after his abysmal start to life at the club.
However, QPR levelled moments later when Bobby Zamora poked the ball home after Djibril Cisse's penalty was saved.
"We'll take the positives out of it because we were very poor last weekend," R's manager Mark Hughes told the club website.
"It was important that we showed up today and I thought we did that. It was a game of few chances in fairness, but in terms of our organisation and quality it was a vast improvement."
Hughton echoed Hughes' sentiments, calling Norwich's performance a 'response' to last weekend's thrashing.
"I thought the players responded after what happened at Fulham with a much better performance and the only slight disappointment is it's definitely a game we should have won," Hughton told the club website.
"We were certainly looking for a big improvement in terms of performance. We asked them to give us a performance today and they have done that."
The game between Sunderland and Reading was called off due to a waterlogged pitch.
"There has been a lot of rain. We arrived here about the same time as Reading and the referee had serious doubts in his mind," Sunderland manager Martin O'Neill explained to the club website.
"It's the right decision to make but it's a blow to us."