Liverpool, Stoke City and Sunderland all recorded their first Premier League wins of the season as Chelsea got the better of Arsenal in a London derby.
Reading are still searching for their first three points of the campaign after last season's Championship winners were twice pegged back by Newcastle United, while Tottenham Hotspur hung on for a famous victory at Manchester United.
Champions Manchester City came from behind to overcome Fulham at Craven Cottage, while Everton also recovered from a slow start to see off Southampton.
Chelsea inflicted a first defeat of the season on Arsenal after a 2-1 win at Emirates Stadium maintained their unbeaten start and position at the head of the table.
Laurent Koscielny endured an afternoon to forget and poor defending from the Frenchman on 20 minutes allowed Fernando Torres to hook home Juan Mata's free-kick for the opening goal.
Arsenal levelled three minutes before half-time when substitute Alex Oxlade-Chamberlain's low ball into the box was controlled and finished superbly by Gervinho in an instant.
However, the Blues scored the winner eight minutes into the second half when Mata's curling free-kick into the box was deflected beyond Vito Mannone by Koscielny.
Tottenham Hotspur withstood a second-half onslaught from Manchester United to win 3-2 and claim a first league victory at Old Trafford since 1989.
The visitors, who have been improving steadily under Andre Villas-Boas, took the lead after just two minutes when defender Jan Vertonghen's shot deflected in off Jonny Evans.
Spurs continued on the front foot and were 2-0 ahead before half-time when Gareth Bale left Rio Ferdinand trailing in his wake before steering his shot beyond Anders Lindegaard.
United introduced Wayne Rooney at half-time and pulled a goal back on 51 minutes when Nani scored, only for Spurs to restore their cushion within 60 seconds when Clint Dempsey pounced after Lindegaard had pushed out Bale's shot.
Yet within a minute, United were back in it after Robin van Persie fed Shinji Kagawa and the Japan international turned smartly before firing past Brad Friedel.
United threw everything at Spurs in search of an equaliser, with Rooney and Michael Carrick hitting the woodwork and Van Persie having a goal ruled out for offside.
Substitute Edin Dzeko made an immediate impact as he scored a late winner as Manchester City came from behind to beat Fulham 2-1 at Craven Cottage.
Fulham took a 10th minute lead when Mladen Petric sent Joe Hart the wrong way from the penalty spot after Pablo Zabaleta had brought down John Arne Riise, with City claiming the foul was outside the area.
Mark Schwarzer kept City at bay for much of the first half, but was finally beaten two minutes before the interval when Sergio Aguero turned home after Carlos Tevez's deflected shot had been pushed out.
City's comeback was complete with just three minutes left to play when Fulham failed to deal with Gael Clichy's cross and Dzeko thumped the ball into the top corner just moments after replacing Javi Garcia.
Luis Suarez scored a hat-trick at Carrow Road for the second season in a row as Liverpool claimed a first Premier League victory under Brendan Rodgers by thumping Norwich City 5-2.
Liverpool were in front with barely a minute on the clock when the ball bounced out to Suarez on the edge of the area and he drilled a low right-footed shot past John Ruddy.
Simeon Jackson was denied by the post for Norwich before 10 minutes were even on the clock, while Suarez was unfortunate not to be awarded a penalty when he was bundled to the ground by Leon Barnett.
Suarez increased the Reds' advantage seven minutes before the break when he pounced on hesitant defending to win possession and flick an excellent shot beyond Ruddy, having missed a much simpler chance moments earlier.
The visitors flew out of the blocks in the second half as well and made it 3-0 when Nuri Sahin had an easy finish from Suarez's pass after the Uruguayan's initial cross had come back to him.
Suarez then completed his hat-trick on 56 minutes with a curling effort from 25 yards before the Canaries pulled a goal back through Steve Morison after Pepe Reina had failed to hold Russell Martin's shot.
But any hopes Norwich may have had of a remarkable comeback were quickly extinguished when Liverpool captain Steven Gerrard's shot from the edge of the area was deflected beyond a deceived Ruddy.
There was some late cheer for the home fans, though, as Grant Holt came off the bench to score his first goal of the season after placing his shot beyond Reina's reach.
Nikica Jelavic scored a first-half brace as Everton recovered from a sluggish start to beat Southampton 3-1 at Goodison Park.
Southampton enjoyed a dream start on Merseyside as record signing Gaston Ramirez had the simple task of heading home at the far post after Everton keeper Tim Howard had misjudged a corner.
But Everton rallied and drew level on 25 minutes when Leon Osman smashed home after Kevin Mirallas' cross fell kindly for the midfielder.
Jelavic then put Everton firmly in control before half-time as he fired home an angled drive on 32 minutes before heading home Seamus Coleman's cross six minutes later.
Demba Ba scored a disputed late equaliser as Newcastle United denied Reading a first league win of the season following a 2-2 stalemate.
After a desperate first half at the Madejski Stadium, the match was livened up by a spell of three goals in the space of four minutes.
Reading took the lead on 58 minutes when Jimmy Kebe slipped upon shooting to wrong-foot Steve Harper, but the Magpies were level within a minute when Ba volleyed home in stunning fashion from Cheick Tiote's searching pass.
However, the Royals regained the initiative on 62 minutes when Jobi McAnuff did well down the left and his cross was glanced inside the far post by Noel Hunt.
Ba helped to draw Newcastle level again on 83 minutes, although this time in more controversial circumstances as Shane Ferguson's cross hit the Senegal striker's arm before deflecting in off Kaspars Gorkss.
Peter Crouch scored a first-half double as Stoke City picked up three points for the first time this term after a 2-0 home success over out-of-form Swansea City.
Stoke edged ahead on 12 minutes when Crouch was given too much room six yards out to stoop and head home a corner from the left.
Crouch doubled the Potters' lead on minutes when he reacted smartly to tap home the loose ball after his initial shot had been pushed out by Swansea keeper Michel Vorm.
Steven Fletcher continued his excellent start to his Sunderland career by scoring the only goal of the game against 10-man Wigan Athletic at the Stadium of Light.
Wigan had been the better team in the first half, but the match swung in Sunderland's favour in the space of three minutes early in the second half.
Firstly, Wigan midfielder Jordi Gomez was sent off for lunging in on Danny Rose on 48 minutes before the in-form Fletcher put Sunderland in front by steering home James McClean's cross-shot.