Crystal palace 0-1 Chelsea
Hakim Ziyech scored a late goal to give Chelsea a 1-0 victory against Crystal Palace at Selhurst Park.
Thomas Tuchel's team has moved seven points ahead of fourth-placed Manchester United, who face Leeds on Sunday with the potential to reduce the gap.
Vicente Guaita made a great stop from Antonio Rudiger after the German took aim from 40 yards out and unleashed a diverting rocket of a shot towards the top corner, which the Spaniard palmed away.
After Christian Pulisic was dispossessed and maybe fouled in midfield, the hosts had their finest opportunity in first-half stoppage time. With a clever through pass, Olise broke and put Wilfried Zaha in, but the Ivorian could only plant his finish wide from the angle.
Chelsea didn't improve after the half, and the game seemed to be trudging along to a 0-0 draw without incident.
Arsenal 2-1 Brentford
Arsenal kept their Champions League qualifying hopes alive with a 2-1 win against Brentford at the Emirates Stadium thanks to second-half goals from Emile Smith Rowe and Bukayo Saka.
Liverpool 3-1 Norwich
Mohamed Salah scored his 150th goal for Liverpool, while Sadio Mane and Luis Diaz also scored, as the Reds rallied to defeat Norwich and maintain pressure on league leaders Manchester City.
Salah scored seconds later with a calm finish after a magnificent 70-yard ball from Alisson, with new signing Diaz completing the scoring by tucking away Jordan Henderson's slide-rule pass.
Manchester City 2-3 Tottenham
After guiding Tottenham to a dramatic 3-2 victory at Etihad Stadium, Harry Kane showed Manchester City exactly what he can give by opening the championship race wide open.
The England striker capped an incredible individual game with a second-half double after being extensively linked with a big-money transfer to the champions in the summer.
Despite the setback, City was mostly dominating and levelled shortly after the half-hour mark when Hugo Lloris failed to hold on to Raheem Sterling's cross, enabling Ilkay Gundogan to score.