Leaders Chelsea snatched a 2-1 win at Blackburn Rovers through a late Branislav Ivanovic strike and Alex Song's 88th-minute header secured a 1-0 win for Arsenal over West Ham United.
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Chelsea lead the table with 25 points from 10 games, five ahead of Arsenal and United and eight clear of City.
Blackburn were well on top of a lacklustre Blues side in the early stages and took a deserved lead through Benjani Mwaruwari after 21 minutes before the visitors hit back through Nicolas Anelka six minutes before halftime.
Chelsea, held 1-1 by Blackburn last season, eventually awoke from their torpor and even though they struggled to create chances they found a way through when Yuri Zhirkov's cross was headed home by Ivanovic after 84 minutes.
Arsenal dominated possession at the Emirates, hitting the woodwork twice, but had to wait until the 88th minute to find a way past obdurate West Ham as Gael Clichy crossed for Song to nod in his third goal in a week.
"Song is amazing, he has added something to his game. He came as a centre back, becomes a defensive midfielder and now he's playing like a striker," said Arsene Wenger.
Manchester City were all over Wolves initially but after a 23rd-minute Emmanuel Adebayor penalty they sat back and paid a heavy price when Nenad Milijas equalised and David Edwards scrambled in a winner after 57 minutes.
Elsewhere, Yakubu's second half goal was enough to see Everton overcome Stoke City 1-0, while Clint Dempsey scored twice to see Fulham to a 2-0 home victory over Wigan Athletic.
