Chelsea's Champions League qualification hopes were bolstered as a 3-2 victory over Crystal Palace moved them into third in the Premier League table while Brendan Rodgers' Leicester City left it late to snatch a 1-1 draw at Arsenal.
City are in fourth spot, one point behind Chelsea and four ahead of Manchester United who have played a game less.
Olivier Giroud, Christian Pulisic and substitute Tammy Abraham netted for Frank Lampard's side.
In the late kick off, Pierre-Emerick Aubameyang's 20th league goal of season looked set to sink the Foxes until Jamie Vardy struck in the 84th minute to foil the hosts who had Eddie Nketiah sent off with 15 minutes left.
Meanwhile, Norwich City, including Northern Ireland internationals Jamal Lewis and Michael McGovern, will be relegated if they lose to West Ham on Saturday.