(CNN) -- An 87th minute header from beleaguered striker Andy Carroll handed Liverpool a 2-1 victory over Merseyside rivals Everton in the semifinal of the English FA Cup on Saturday.
Carroll's effort compounded a miserable second half for David Moyes' team after a promising opening to the match played at Wembley Stadium.
Nikica Jelavic pounced on a mix up between Liverpool defender's Jamie Carragher and Daniel Agger in the 24th minute to side-foot past goalkeeper Brad Jones to hand Everton the lead.
It stayed that way until the 62nd minute when Sylvain Distin's sloppy back-pass gifted Liverpool a way back into the game.
Luis Suarez raced onto the mistake before comfortably beating Tim Howard with the outside of his right boot to level the scores.
Liverpool perhaps should have been ahead earlier in the half when Andy Carroll missed a gilt-edged chance to equalize but somehow directed his header wide.
But the $55 million man made amends rising above Everton's Marouane Fellaini to nod home the winner from a Craig Bellamy free-kick.
"It's the best feeling ever. We worked hard and getting the goal right there at the end was great," Carroll told ESPN afterwards.
"I had a few chances and should have probably scored earlier. But I kept at it and it was a great ball in by Craig (Bellamy), and I just had to score with that one and I did.
"It's a great feeling. I've had some criticism but I've just kept on going," Carroll added.
His manager Kenny Dalglish, who has also been the subject of criticism after Liverpool's poor league form in recent weeks, was delighted with the effort of his team.
"I think it was fantastic and although it's not been too good in the league recently, that's two cup finals -- one we've won and won we're looking forward to," Dalglish told ESPN.
Chelsea take on Tottenham Hotspur in the second semifinal on Sunday. The final will be played on Saturday May 5.
Meanwhile in the English Premier League, Carlos Tevez scored a hat-trick for Manchester City on Saturday in the English Premier League as Manchester City thrashed Norwich City 6-1 at Carrow Road.
The win closes the gap on leaders Manchester United to just two points who play Aston Villa at Old Trafford on Sunday.
The Argentine put City ahead in the 18th minute, before his compatriot Sergio Aguero added a second nine minutes later.
Andrew Surman's goal for Norwich six minutes after the break gave home fans hope of a comeback but four goals from City in the final quarter of the match killed off the game.
Tevez bagged his second in the 73rd minute as did Aguero two minutes later to make the game safe.
Tevez, who was starting only his second league game since last September, claimed his hat-trick ten minutes from the end, with Adam Johnson completing the rout in injury time to boost City's goal difference to plus 58, eight ahead of United.
In the other three Premier League fixtures played Saturday, the teams struggling at the foot of the table all had days to forget.
Wolverhampton Wanderers played out a goalless draw against Sunderland at the Stadium of Light -- a result that does little to alleviate their plight at the bottom of the league.
Second-from-bottom Blackburn Rovers were beaten 3-0 by Swansea City, while 16th-placed Queens Park Rangers went down 1-0 against West Bromwich Albion at the Hawthorns.