A brace from Juan Mata in an action-packed contest on Merseyside allowed Louis van Gaal's side to cement their spot in the top four, enhancing their chances of securing Champions League football for next season.
Mata's clinical 14th-minute finish with his right foot preceded a stunning side volley on his left just before the hour-mark as Liverpool played the second half with ten men following Steven Gerrard's mindless red card for a stamp on Ander Herrera.
Daniel Sturridge managed to pull one back for the Reds in the 69th minute despite the discrepancy in personnel before Simon Mignolet saved an injury-time penalty from Wayne Rooney but the damage had already been done.
Early goals from Eden Hazard and Diego Costa were cancelled out by Ahmed Elmohamady and Abel Hernandez before the half-hour mark but substitute Loic Remy won it for the Blues with just over 10 minutes left.
Reigning champions City returned to form with a comfortable 3-0 triumph over ten-man West Bromwich Albion at the Etihad Stadium thanks to goals from Wilfried Bony, Fernando and David Silva while Arsenal made it wins for all top four sides by edging Newcastle United 2-1 at St James' Park.
It was a nervy second half for the Gunners after Olivier Giroud's double in the first lot of 45 minutes had them in cruise control but the Magpies hit back through Moussa Sissoko before having the better of the chances.
Elsewhere, Harry Kane celebrated his England call-up by netting a hat-trick in Tottenham's 4-3 victory over bottom-placed Leicester City who were served by a David Nugent brace but still remain in deep relegation trouble.
Bafetimbi Gomis again stepped into the role vacated by City striker Bony by scoring the only goal of Swansea City's 1-0 win at Aston Villa as Southampton got the better of Burnley 2-0 at home and Wilfried Zaha netted the eventual winner as Crystal Palace nosed out Stoke City 2-1.
West Ham United required a very late goal from Diafra Sakho to defeat Sunderland 1-0 in east London and QPR dominated but were unlucky to lose 2-1 to Everton in west London as Seamus Coleman and Aaron Lennon scored either side of Eduardo Vargas' leveler.
2014/15 Barclays Premier League - season scores
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