Manchester City and Manchester United both picked up their fifth Premier League wins of the season to stay top of the table, with Pep Guardiola's men only ahead of their rivals on goal difference.
Raheem Sterling scored twice inside eight minutes to hand Manchester City a 5-0 victory over rock-bottom Crystal Palace, who are still looking for their first points and goals of the season.
City first found the back of the net on the stroke of half-time through Leroy Sane, who lifted the ball over Scott Dann before finishing at the near post.
And Sane was involved again as City doubled the lead shortly after the break at the Etihad Stadium, teeing up Sterling for a simple finish.
Sterling then scored his second of the afternoon in the 59th minute, this time slotting home following Sergio Aguero's ball into his path, before Aguero got in on the act himself notching a 79th-minute header from Sane's cross. There was still time for a fifth in the 89th minute, with Fabian Delph also getting his name on the score sheet.
Romelu Lukaku scored the only goal of the game as Manchester United saw off Southampton 1-0 at St Mary's, though the visitors had manager Jose Mourinho sent off late on.
Lukaku broke the deadlock after 20 minutes, with the Belgium international slotting home the rebound after his initial effort was saved by Fraser Forster for his sixth league goal of the season.
United were unable to add to that tally in the second half and the game ended with Mourinho being sent to the stands for encroaching on the pitch.
Chelsea remain three points back in third after beating Stoke 4-0 at the bet365 Stadium, with Alvaro Morata scoring a hat trick to secure a third straight away win for the Blues.
Chelsea opened the scoring inside just 90 seconds with Cesar Azpilicueta playing a ball over the top to Morata, who raced in on goal and slotted home.
Pedro added a second on the half-hour mark, finding the bottom corner after latching onto a loose ball, before Morata bagged his second 12 minutes from time, scoring from a tight angle after beating two men.
The Spain international then completed his hat trick eight minutes from the end, with Azpilicueta teeing him up once more and the striker picking out the back of the net.
Simon Mignolet turned away a Jamie Vardy penalty to ensure Liverpool held on for a 3-2 victory over Leicester at the King Power Stadium.
Liverpool opened the scoring in the 16th minute, with Mohamed Salah arriving at the far post to head home Philippe Coutinho's cross, before Coutinho got in on the act himself, bending a fine free kick into the corner seven minutes later.
Leicester pulled one back on the stroke of half-time, with Shinji Okazaki bundling home from close range from a corner, only for Jordan Henderson to restore the visitors' two-goal advantage in the 68th minute, slotting past Kasper Schmeichel following a counterattack.
Leicester pulled one back again a minute later as Jamie Vardy nodded in at the far post, but just a few minutes on the England international saw his penalty turned away by Mignolet after he had been brought down by the Liverpool keeper.
Harry Kane kept up his impressive scoring record against West Ham with his brace inspiring 10-man Tottenham to a 3-2 victory at the London Stadium.
Kane netted twice in the space of four first-half minutes to take his tally against the Hammers to seven goals in his last six Premier League games.
Javier Hernandez pulled one back for West Ham after Christian Eriksen had made it three, but despite Sergie Aurier picking up a red card and Cheikhou Kouyate netting late on, the hosts were unable to stage a comeback.
Oumar Niasse scored twice as Everton came from behind to beat Bournemouth 2-1 at Goodison Park and move out of the relegation zone.
After a first half of few chances, Bournemouth moved ahead shortly after the restart, with Joshua King lashing a strike into the bottom corner after receiving the ball off Charlie Daniels.
But on 77 minutes Niasse popped up to rifle home after Tom Davies had picked him out, before he then added a second five minutes later to ensure Everton took home all three points.
Richarlison netted a last-minute winner for Watford to secure a 2-1 victory over Swansea at the Liberty Stadium.
Watford edged ahead in the 13th minute through Andre Gray, who smashed in a loose ball following Andre Carrillo's cross to net his first goal for the club.
Swansea levelled proceedings after 56 minutes, with Tammy Abraham netting a simple finish from close range, only for Richarlison to beat Lukasz Fabianski at the death to give his side the victory.
Burnley and Huddersfield played out a 0-0 draw at Turf Moor.
Burnley went closest to scoring in the first half with Chris Wood's header from Stephen Ward's cross landing just wide of the target, while Huddersfield were denied by a Nick Pope save in the second period, with Laurent Depoitre being thwarted.