Manchester United produced a familiar comeback to deny Hull City boss Steve Bruce a first win against his former club, while Crystal Palace climbed out of the relegation zone after beating Aston Villa.
Chelsea continue to be efficient rather than entertaining after seeing off Swansea City, but Everton suffered a first home defeat of the season after being stunned by Sunderland.
Tottenham Hotspur were held at home by West Bromwich Albion, while Newcastle United stuck five past a Stoke City side reduced to nine men in the first half.
Southampton piled further misery on Cardiff City after a convincing win in south Wales, while Fulham snatched a late win at Norwich City.
Liverpool slipped down to fourth in the table after Alvaro Negredo's goal in first-half stoppage-time earned Manchester City a 2-1 win at the Etihad Stadium in a pulsating game.
In a match where the tempo never seemed to cease, Liverpool took the lead on 24 minutes following an excellent move which resulted in Philippe Coutinho finishing from a narrow angle after Raheem Sterling had taken the ball round Joe Hart.
However, City levelled on 31 minutes when Vincent Kompany met a corner at the near post and Joe Allen was unable to prevent the Belgian's header from crossing the line.
The winner came in added time at the end of the first half when a superb pass from Jesus Navas, who had hit the post after just five minutes, released Negredo and his shot with the outside of his left foot crept over the line after Liverpool goalkeeper Simon Mignolet only got a weak hand to the ball.
Liverpool pressed for an equaliser in the second half, with Sterling blazing a golden chance over and Luis Suarez unlucky not to get a penalty after his shirt was tugged by Joleon Lescott.
Theo Walcott continued his impressive scoring record against West Ham United as Arsenal came from a goal down to win 3-1 at Upton Park.
West Ham went in front inside the opening minute of the second half when Arsenal keeper Wojciech Szczesny failed to hold Kevin Nolan's shot and Carlton Cole snaffled up the loose ball.
Arsenal equalised on 68 minutes when Walcott scored against West Ham for the fourth Premier League game in a row as he cut inside and fired a low shot past Adrian.
Just three minutes later and Walcott had given Arsenal the lead when he headed Lukas Podolski's deflected cross beyond Adrian.
Podolski then capped his first appearance since the end of August with the third goal as he drilled home on 79 minutes after being teed up by Olivier Giroud.
Jose Mourinho's unbeaten home record in the Premier League was maintained after Eden Hazard's first-half goal earned Chelsea a 1-0 win over Swansea City at Stamford Bridge.
Chelsea scored on 29 minutes when Hazard cut into the box from the left flank and his powerful shot found its way past Gerhard Tremmel, who had possibly been unsighted by the ducking Ashley Williams.
Manchester United were indebted to former defender James Chester for a fifth win in a row in all competitions after coming from 2-0 down to beat Hull City 3-2 at the KC Stadium.
Chester, who made one substitute appearance for United before joining Hull nearly three years ago, put the Tigers ahead after just four minutes by lashing home the ball after the visitors had defended poorly from a corner.
More sloppy defending from United contributed to Hull's second goal on 13 minutes when David Meyler was given a second chance to shoot and his scruffy shot deflected off Jonny Evans and past David de Gea.
However, United equalised within six minutes when Wayne Rooney curled in a free-kick from the right and Chris Smalling rose well to guide home his header.
Rooney equalised for the Red Devils on 26 minutes when he took one touch to control the ball before volleying a stunning shot from 30 yards beyond Allan McGregor.
The decisive goal arrived on 66 minutes when Ashley Young crossed from the right and Chester headed into his own net as Rooney lurked menacingly behind him.
United had Antonio Valencia sent off for a second yellow card in added time and there was still an opportunity for Chester to snatch a point, but the defender was denied by De Gea.
Tim Sherwood's first home game since being confirmed as Tottenham's permanent manager ended in a 1-1 draw after West Brom hit back to take a point at White Hart Lane.
Tottenham took the lead on 36 minutes through Christian Eriksen's first Premier League goal when the Denmark international curled a brilliant free-kick over the wall which bounced in off the underside of the crossbar.
But West Brom were level within two minutes when the Spurs defence failed to clear a free-kick and Jonas Olsson stabbed home from close range.
Malky Mackay's position as Cardiff manager is likely to come under further scrutiny after owner Vincent Tan was in the directors' box to see a 3-0 home defeat by Southampton, who ended a run of six games without a win.
Southampton capitalised on some woeful defending by Cardiff in the first half and took the lead on 14 minutes when Adam Lallana's cross was finished off at the far post by the unmarked Rodriguez.
England international Rodriguez scored his second of the game six minutes later when he was allowed to get on to the end of Rickie Lambert's cross far too easily before scoring past David Marshall.
And Cardiff's inability to deal with another ball into the box led to the third goal on 27 minutes when the home side failed to clear before Lambert steered his shot past Marshall.
Bottom club Sunderland recorded a first away win of the season after winning 1-0 at Everton, who had goalkeeper Tim Howard dismissed in the first half.
Everton were reduced to 10 men on 23 minutes when Howard was sent off for bringing down Ki Sung-yueng in the box after the South Korean had seized on a poor piece of control from Leon Osman.
Joel replaced Howard in goal and he was unable to prevent Ki from scoring the resulting penalty after the midfielder placed his spot-kick inside the post.
Newcastle posted a seventh win in nine games to remain in the hunt for UEFA Champions League qualification after a 5-1 dismantling of nine-man Stoke at St James' Park.
Stoke forged in front just before the half-hour mark when the ball fell to Oussama Assaidi on the corner of the box and the on-loan Liverpool winger cut in on his right foot before curling a fine effort beyond Tim Krul.
But the game swung in Newcastle's favour in a flurry of activity five minutes before half-time when Stoke midfielder Glenn Whelan was sent off for a second bookable offence before Marc Wilson followed him down the tunnel after being shown a red card for pulling back Loic Remy in the box.
Remy saw his penalty saved by Thomas Sorensen, but the France international made amends a minute before half-time when his shot deflected off Ryan Shawcross to draw Newcastle level.
Newcastle turned the screw after half-time and took the lead on 48 minutes when Yoan Gouffran drove home from the edge of the box after a poor punch by Sorensen from Hatem Ben Arfa's cross, although there was a suspicion that the ball may have gone out of play.
Ben Arfa then struck the upright before Newcastle scored a third on 56 minutes when Remy pounced at the far post after Moussa Sissoko had failed to apply the finishing touch to Mathieu Debuchy's cross.
A fourth goal arrived on 66 minutes when Yohan Cabaye was teed up on the edge of the area and the midfielder curled an excellent first-time shot inside the post.
Newcastle chalked up a fifth goal with 10 minutes to go when Erik Pieters brought down Ben Arfa in the box, with substitute Papiss Cisse handed the penalty-taking duties on this occasion, and the striker duly obliged.
Scott Parker smashed home an 87th-minute winner to give Fulham boss Rene Meulensteen his first away success following a 2-1 triumph at Norwich.
Gary Hooper put Norwich in front on 13 minutes when scoring for the fourth successive home game after his 30-yard shot hit Aaron Hughes and looped over Fulham keeper David Stockdale.
Fulham had a goal disallowed when Norwich keeper John Ruddy's clearance struck Parker's arm, but the visitors were level on 33 minutes when Pajtim Kasami fired a 30-yard free-kick through the Canaries wall.
With three minutes to go, Fulham stole the points when the ball was cleared to Parker 30 yards out and he thundered a drive beyond the dive of Ruddy.
Substitute Dwight Gayle scored a sumptuous last-minute winner as Crystal Palace beat Aston Villa 1-0 away from home to move out of the bottom three.
Former Villa midfielder Barry Bannan had been denied by Brad Guzan and the post before Gayle cut in on his right foot to curl a brilliant shot into the top corner.