The Gunners remained fifth but are just two points out of the top four with a game in hand on fourth-placed North London rivals Tottenham after beating West Bromwich Albion 2-1 at The Hawthorns.
Tomas Rosicky, in just his second start of the campaign, had not scored in the league since February last year but managed a double as Arsene Wenger's men had to deal with the sending off of Per Mertesacker prior to James Morrison's 71st minute penalty.
Chelsea were also fortunate in their victory as they trailed Sunderland by a goal at the break following Cesar Azpilicueta's own-goal but were back on level terms early in the second half when Matthew Kilgallon inadvertently sent the ball into the back of his own net after a deflection off goalkeeper Simon Mignolet.
Chelsea then hit the lead five minutes before the hour-mark when Branislav Ivanovic cleverly diverted David Luiz's effort in for the winner. The Blues went back to third after Tottenham drew 2-2 with Everton at White Hart Lane.
Spurs struck early through Emmanuel Adebayor but goals from Phil Jagielka and Kevin Mirallas edged the Toffees in front before Gylfi Sigurdsson levelled it late for the home side who are now on 58 points from 32 outings and in danger of relinquishing fourth spot to the Gunners.
The Reds were held to a 0-0 draw at Anfield by West Ham United but managed to go five points ahead of eighth-placed West Brom.
Reading's relegation woes got even worse when they were beaten 2-0 at home by Southampton, who pushed up to 11th, whilst Swansea City squandered a one-goal lead before scoring 15 minutes from time to force a 2-2 draw at Norwich City.
Goals from Gabby Agbonlahor, Matthew Lowton and Christian Benteke allowed Aston Villa to record a vital 3-1 victory at Stoke City, pushing them two points clear of the drop zone, and sending the Potters down to 15th.
Papiss Cisse produced his third-straight injury-time winner as Newcastle United edge Fulham 1-0 at St James' Park whilst QPR were unlucky to be held to a 1-1 draw by Wigan Athletic despite striker Bobby Zamoras being sent off.
To finish off the weekend's round of matches, Manchester United will be looking to extend their lead at the top of the standings from 15 points to 18 over reigning champions Manchester City when they clash at Old Trafford on Monday night.
2012/13 Barclays Premier League season scores