Arsenal were handed a shock 1-0 defeat by Belarusian outfit BATE Borisov in the first leg of their UEFA Europa League Round of 32 fixture on Thursday.
A Paul Pogba double and an Anthony Martial strike fired Manchester United to a comfortable 0-3 win over Fulham on Saturday afternoon.
A hat-trick from Sergio Aguero condemned Arsenal to a 3-1 defeat against Manchester City at the Etihad Stadium on Sunday.
Marcus Rashford's early strike was enough to hand Manchester United all three points in their away match against Leicester City.
Eden Hazard and Gonzalo Higuain both grabbed a brace as Chelsea bounced back strongly from their midweek defeat, beating Huddersfield Town 5-0.
Anthony Martial has renewed terms with Manchester United, having signed a new long-term contract that ties him up at Old Trafford till June 30, 2024.
Manchester United were made to work hard for all three points by Brighton & Hove Albion, who were beaten 2-1 by Ole Gunnar Solskjaer's men at Old Trafford on Saturday.
Liverpool came back from being a goal down in the first-half to defeat Crystal Palace 4-3 at home to extend their lead at the top of the Premier League table.
A Mohamed Salah penalty was the difference between Brighton and Liverpool, who returned to winning ways with a crucial 1-0 success at the Amex Stadium on Saturday.
Cesc Fabregas has completed his move from Chelsea to AS Monaco, with the struggling Ligue 1 outfit signing the Spaniard on a three-and-a-half year deal.