Liverpool secured a dominant win over West Ham, while other Premier League matches saw Brentford edge Burnley in a seven-goal thriller and Everton secure a late victory against Newcastle.
Chelsea had looked in full control at halftime after goals from Marc Cucurella and Cole Palmer
Manchester City's spending of more than 180 million pounds ($223.58 million) was the second-biggest outlay ever worldwide by a club in the January transfer window.
Ruthless Arsenal threw down the gauntlet in the Premier League title race with a 5-0 thrashing of London rivals Chelsea to roar three points clear at the top of the table on Tuesday.
Manchester United languish 14th in the standings on 19 points, their worst placing to end a calendar year since they were 15th in 1989.
IMAGES from the English Premier League matches played on Sunday
Liverpool's slim Premier League title hopes faded further on Saturday when Michail Antonio's late header earned West Ham United a deserved point with a 2-2 draw.
IMAGES from the English Premier League matches played on Wednesday.
Manchester City's Kevin de Bruyne sparked a late comeback 3-2 victory for his side at Newcastle United.
Liverpool snatched three points with a wild 1-0 victory over relegation-threatened Nottingham Forest.
The season-openers for champions Paris St Germain and Olympique Lyonnais were postponed after both teams reached the Champions League semi-finals.
The Tunisian captain's goal mobilised the French into action, with Deschamps bringing in stars like Kylian Mbappe and Antoine Griezmann to jump-start an attack that had so far been tepid.
Manchester United climb into sixth place with 3-0 West Ham win