Manchester City's first win at Anfield since 2003 left them top of the Premier League by five points and effectively knocked Liverpool out of the title race on Sunday.
Ilkay Gundogan scored twice in the 4-1 rout of the champions in which Liverpool keeper Alisson suffered a horrible afternoon, making two dreadful errors to gift City two goals.
Meanwhile, Chelsea's new coach Thomas Tuchel claimed his third win in four games since taking over from Frank Lampard, his side edging out bottom club Sheffield United 2-1 at Bramall Lane thanks to a strike by Mason Mount and a penalty by Jorginho.