Manchester City won 2-1 at Aston Villa.
Hakim Ziyech’s first Premier League goal of the season kept injury-hit Chelsea top of the table after a tense 2-1 win at Watford
The Morocco forward side-footed into the roof of the net from Mason Mount’s cross, after the midfielder had earlier slotted Chelsea’s opener.
Emmanuel Dennis’ fourth goal in five Premier League games had Claudio Ranieri’s Hornets level and the hosts caused the reigning European champions all manner of problems.
But Thomas Tuchel’s men edged to victory despite missing a clutch of injured regulars, to cling onto a one-point lead at the Premier League’s summit.
Pep Guardiola’s men retained second place in the table courtesy of another potent showing, though Steven Gerrard’s Villa were on target through Ollie Watkins’ fine finish.
The red-hot Mohamed Salah took his Premier League goals tally to 13 for the campaign with a match-winning brace in Liverpool’s 4-1 win in the Merseyside derby.
The Egypt hitman twice provided cool finishes to subdue Everton at Goodison Park, after captain Jordan Henderson had curled the Reds into an early lead.
Diogo Jota added a late fourth to put the icing on the cake for Jurgen Klopp’s side, who still sit third in the table.
Demarai Gray had earlier latched onto Richarlison’s pass before notching for Everton, but Rafael Benitez’s men were well beaten in the end as the fans poured out of Goodison in disappointment.
Southampton and Leicester played out an exciting 2-2 draw on the south coast, with Jan Bednarek and Che Adams on target for the hosts.
Jonny Evans slotted home for Leicester, before James Maddison conjured a fine equaliser to steal the Foxes a point.
The games at Watford and Southampton were both delayed due to supporters requiring emergency medical attention.
Tomas Soucek thought his early header would be enough for West Ham to see off Brighton, only for Neal Maupay’s overhead kick to snatch an 89th-minute equaliser in a 1-1 draw in east London.
Wolves and Burnley played out a goalless stalemate at Molineux.