Referee Neil Swarbrick blew for a foul on Wilfried Bony by Craig Dawson but incorrectly dismissed Gareth McAuley.
Bony, Fernando and David Silva netted for City.
Elsewhere, two goals from Olivier Giroud handed Arsenal a 2-1 win at Newcastle, while Harry Kane hit his first Premier League hat trick as Tottenham beat Leicester 4-3.
Southampton beat Burnley 2-0 at St. Mary's to maintain its push for European football next season.
Crystal Palace came from behind to win 2-1 at Stoke while Bafetimbi Gomis scored in the 87th minute to give Swansea a 1-0 win over Aston Villa.