Liverpool players celebrating
Liverpool scored two goals in three second-half minutes as they fought back from 2-1 down to beat West Ham thanks to a late James Collins own goal, while at Goodison Park a late goal by Nikica Jelavic ensured that Everton grabbed all three points in their game with Spurs.
At Upton Park, the Reds took an early lead through a spectacular Glen Johnson strike.
Mark Noble equalised from the spot after Joe Allen handled and Steven Gerrard headed into his own net to put the Hammers ahead at half-time.
But Joe Cole made it 2-2 with an angled drive before Jordan Henderson's cross span in off Collins at the near post.
And two goals in stoppage time produced a dramatic late turnaround at Goodison Park as Everton beat Tottenham to move into fourth spot in the Premier League.
Spurs appeared to be on their way to victory courtesy of Clint Dempsey's deflected 76th-minute strike.
Gylfi Sigurdsson then hit the Toffees crossbar with a shot before Steven Pienaar header in against his former club to equalise after 90 minutes.
Jelavic then turned in a close-range shot for Everton's winner.
Spurs, without the buccaneering Gareth Bale through injury, thought they had produced a classic away performance, having soaked up the home side's pressure before taking the lead through one of their rare forays forward.
Man City 2 - 3 Man Utd
Everton 2 - 1 Tottenham
West Ham 2-3 Liverpool