The Blues took the lead through Fernando Torres' clever finish in the 20th minute at the Emirates Stadium before Gervinho levelled for the Gunners just minutes before half-time but Juan Mata's 53rd minute free-kick was helped into the back of the net by Laurent Koscielny.
The win allowed Chelsea to go three points clear at the summit with Everton sitting in second place following their 3-1 home victory over Southampton which came courtesy of a double from Nikica Jelavic and a 25th minute leveller from Leon Osman after Gaston Ramirez's sixth-minute header.
Champions Manchester City stayed fourth thanks to a late winner from Edin Dzeko which allowed them to complete a come-from-behind 2-1 triumph at Fulham. Mladen Petric converted from the penalty spot in the 10th minute before Sergio Aguero equalised on the stroke of half-time prior to Dzeko's 8th minute winner.
Luis Suarez scored his second hat-trick at Carrow Road in two games to lead Liverpool to a 5-2 away victory over Norwich City. The Uruguayan struck in the second, 38th and 57th minutes and was joined on the scoresheet by summer signing Nuri Sahin and skipper Steven Gerrard to give the Reds their first triumph of the campaign with Steve Morison and Grant Holt netting for the Canaries.
Newcastle United twice came from behind to force a 2-2 draw with Reading at the Madejski Stadium thanks to a second-half brace from Demba Ba after Jimmy Kebe scored the opener and then Noel Hunt gave the home side the go-ahead just after the hour-mark. The draw put the Magpies into ninth as the Royals moved off the bottom and into 19th.
Stoke City opened their winning account for the season as they beat Swansea City 2-0 at home via a brace from Peter Crouch to make it three losses in a row for the Welsh club whilst Steven Fletcher's fifth strike of the season allowed Sunderland to beat ten-man Wigan Athletic 1-0 at the Stadium of Light who had Jordi Gomez sent off early in the second half.
Tottenham managed to break a 23-year hoodoo at Old Trafford by beating Manchester United 3-2 in an enthralling contest at the Theatre of Dreams.
Spurs opened the scoring inside two minutes through new defender Jan Vertonghen before Gareth Bale added a second just after the half-hour mark. Six minutes into the second half, Nani got one back for United but Clint Dempsey made it 3-1 in the 52nd minute with his first goal in a Spurs shirt.
Shinji Kagawa gave United hope with a second goal for the home side moments later but it was enough as Andre Villas-Boas got the better of Sir Alex Ferguson to see his side go fifth wit last season's runners-up falling to third.
In Sunday's only fixture, Aston Villa scored a late goal through Darren Bent to force a 1-1 draw with West Bromwich Albion in the West Midlands derby and to wrap up the sixth week of action, QPR host London rivals West Ham United at Loftus Road on Monday night.
2012/13 Premier League scores