(CNN) -- Defending English Premier League champions Manchester City had to come from behind twice to snatch a 2-2 draw at improved Liverpool Sunday.
Liverpool stumbled to a 3-0 defeat at West Bromwich Albion on the opening day of the season, but could count themselves unfortunate not to claim three points at Anfield.
Martin Skrtel headed them ahead from a Steven Gerrard corner after 34 minutes, but the visitors drew level after Yaya Toure capitalized on hesitancy just after the hour mark.
Liverpool responded almost immediately as a long-range free kick from Luis Suarez eluded City goalkeeper Joe Hart to put them 2-1 ahead.
But they could not hold their lead and in the 80th minute Skrtel was the villain as his back pass fell short of Pepe Reina and Carlos Tevez swooped to round the home goalkeeper and equalize.
Both sides had chances to claim three points in a frantic finish with substitute Andy Carroll's header cleared off the line by City's new signing Jack Rodwell.
Joe Allen, one of new manager Brendan Rogers' summer acquisitions, had a fine game on his Anfield debut.
"Here at Anfield the atmosphere was fantastic, as I expected. I'm looking forward to playing here this season.
"The style of Brendan's play is a big, positive factor for everyone, and the players are looking forward to playing under Brendan Rodgers," he told Sky Sports.
Arsenal drew blank for the second straight EPL fixture after being held to a 0-0 draw at Stoke in the earlier kickoff Sunday.
Arsenal, third last season, lost star striker Robin van Persie to rivals Manchester United in the close season and have lacked a cutting edge in their opening two fixtures.
Stoke, who drew 1-1 at Reading in their opener, also have two points after two games to lie 11th in the early table with Arsenal 12th.
"It's never a disaster to win a point at Stoke," Arsenal manager Arsene Wenger claimed after the match, urging patience as his new signing s Olivier Giroud and Lukas Podolski bed in.