Raheem Sterling curled in a last-minute goal to give Manchester City victory over Southampton and extend their Premier League winning run to 12 games.
Mo Salah came off the bench to score twice and secure an ultimately comfortable victory for Liverpool over Stoke that moves Jurgen Klopp's side up to fifth.
Senegal winger Sadio Mane gave the Reds a controversial early lead, dinking the ball into the net after a marginal linesman's call.
Stoke believed Liverpool keeper Simon Mignolet should have been sent off for a challenge just outside the box on their striker Mame Biram Diouf and Mark Hughes' side applied pressure after the break.
Elsewhere, Mesut Ozil inspired Arsenal to a dominant victory over Huddersfield as the Gunners maintained their perfect home record in the Premier League this season.
The midfielder, back in the side after recovering from injury, scored one goal and provided two assists as the hosts made it seven wins from seven at the Emirates.
Also, Wayne Rooney scored a stunning goal from his own half to complete a hat-trick as Everton thrashed West Ham in front of incoming manager Sam Allardyce and Bournemouth lost 2-1 at home to Burnley.