Chelsea stayed seven points clear on top of the English Premier League after a late goal gave them a 1-0 win over Everton at Stamford Bridge.
Willian’s long-range strike in the 89th minute proved the difference as the Blues edged Everton, while City thumped Stoke City 4-1 at the Brittania Stadium.
Sergio Aguero returned to goal-scoring form with a brace against Stoke, while James Milner and Samir Nasri added to the goal collection to cancel out Peter Crouch’s equaliser.
In the race for a top-four spot, Manchester United strengthened its claim with a 3-1 win over Burnley City, with defender Chris Smalling scoring twice.
West Ham United saw goalkeeper sent off for a handball outside the box, but the Hammers managed to frustrate high-flying Southampton in a 0-0 draw.
West Bromwich Albion did its best to pull away from the bottom of the ladder with a 2-0 win over Swansea City, while Crystal Palace drew 1-1 with Newcastle United.
Meanwhile, Paul Lambert was sacked as manager of Aston Villa after a run of 10 winless games took them into the relegation zone.
“Aston Villa Football Club has parted company this evening with manager Paul Lambert,” Villa announced on their website.
“First-team coach Scott Marshall and goalkeeping coach Andy Marshall will continue to prepare the squad for Sunday’s FA Cup tie with Leicester City at Villa Park.”
Lambert, 45, took over in 2012 and led the Midlands club to 15th-place finishes in his first two seasons, but the former Scotland midfielder had come under pressure from fans following a poor run of recent form.
Villa recently went 11 hours without scoring a Premier League goal and supporters unveiled a banner calling for Lambert to leave during their 2-0 loss at fellow strugglers Hull City on Tuesday.
“The club would also like to place on record its thanks to Paul and take this opportunity to wish him every success in the future,” Villa added.
“The club will announce a new manager in due course. There will be no further comment from the club at this stage.”