The game began in controversial fashion after Steve Sidwell - playing his first match returning from a three-match suspension - from was sent off in the 12th minute for a late tackle on Mikel Arteta.
Despite the man advantage, Arsenal failed to find their groove and was forced on the back foot by a determined Fulham side.
The Gunners then went ahead two minutes before the break when Walcott floated a deep free-kick for Laurent Koscielny to head back into the box, where Per Mertesacker was on hand to nod in from close range.
Fulham continued to press despite going a goal down and had a few decent chances, including a Stanislas Manolev goal ruled offside, but Arsenal managed to hold out to claim a crucial 1-0 win to go third in the league table ahead of the clash between fellow rivals Tottenham and Chelsea.
Mark Schwarzer - 7.5
Schwarzer was unlucky to celebrate his 500th Premier League appearance with a loss. He made a decent stops to deny Arsenal but was never really tested by an insipid attack.
Stanislas Manolev - 8
The Bulgarian may not be knowned to many Premier League fans but his performance against Arsenal could warrant him a spot in the Team of the Week. Manolev was constantly giving Monreal and Arteta headaches with his jinking runs up the pitch while holding strong in defence as well.
Phillippe Senderos - 7
Senderos had a few hairy moments when he was pressured in defence but did well enough to keep Arsenal from getting chances in the Fulham box.
Brede Hangeland - 8
Hangeland was typically massive in the air, winning most of the crosses that went his way to keep Arsenal quiet. He was also quick to snuff out any threats in the box, most notably rushing over to block Cazorla from having a free shot on goal in the box.
Kieran Richardson - 7
Richardson's day was made easier partly due to Sagna and Walcott having generally poor days in terms of delivery. He also contributed in attack occasionally with his crosses.
Eyong Enoh - 7
Enoh is proving himself to be a decent defensive midfield with prompt challenges in midfield to ensure that Arsenal had very little time to build up their play.
Steve Sidwell (Off 12') - 6
Sidwell was unfortunate to be sent off for a late challenge on Arteta.
Bryan Ruiz - 6.5
Ruiz was withdrawn into midfield after Sidwell was sent off and did a decenet job tracking back to defend. However, his passes were wayward and his attempts on goal were disappointing.
Urby Emanuelson - 8.5
Seeing Emanuelson jink past the Arsenal midfielders was like seeing an American Football player dodging past opponents. The Dutchman was constantly leaving red shirts in his wake and was one of the best players on the pitch.
Alex Kacaniklic - 8
The former Liverpool trainee shone with his energetic display, constantly moving ahead of others to link up counter attacks.
Dimitar Berbatov - 7.5
Berbatov was always threatening with runs behind the Arsenal defence but was foiled by the offside trap. He also made the effort to help hsi team mates in defence after Sidwell was sent off.
Mladen Petric (On 85') - N/A
Kerim Frei (On 87') -N/A
Woijcech Szczesny - 7
Szczesny was heavily tested despite going up against 10 men and he stood up to it with good reaction saves to deny Fulham.
Bacary Sagna - 4.5
Sagna was poor in attack with his crosses constantly hitting defenders or too near the keeper. With Arsenal lacking in natural width, Sagna needs to improve on this aspect of his game. Other than that, he was given a tough test in defence by Kacaniklic.
Per Mertesacker - 6.5
Mertesacker was on hand to deal with crosses for Berbatov and popped up to score the winning goal for Arsenal.
Laurent Koscielny - 7
The Frenchman showed that he still is the best defender Arsenal has with a steady display at the back in reading the Fulham attack and covering up for his colleagues.
Nacho Monreal - 5
Monreal looked unsteady under pressure with Emanuelson and Manolev constantly hovering around him. Like Sagna, he was also poor in attack with his crosses failing to impress.
Mikel Arteta - 6
Arteta continued his role as the fulcrum for Arsenal and did well passing the ball around but there was little inventiveness from him when it was needed.
Aaron Ramsey - 4.5
Ramsey rushed into many tackles and was deservedly booked for it. He showed little initiative in supporting the attacking despite the extra man advantage and looked generally lethargic.
Tomas Rosicky (Off 71') - 5.5
Despite his recent run of form, Rosicky failed to have an impact on the game but it was not for the lack of trying. He was trying to distribute the ball at the heart of Arsenal's attack but his colleagues were not running into space around him.
Santi Cazorla (Off 90') - 5
Cazorla had an uncharacteristically poor game with many errant passes. He showed little ease out wide - perhaps it was a message to Wenger to put him back into the middle.
Theo Walcott (Off 71') - 5.5
Walcott's speed continued to be a threat for Arsenal down the flank but he was hesitant in the box when the ball came to him and his delivery was poor.
Olivier Giroud (Off 90') - 5
Giroud did well when the ball came to him by linking up play and threatening to find space in the box but he was let down by his team mates, who failed to provide him with a decent supply of passes.
Jack Wilshere (On 71') - 6.5
Arsenal linked up play better when Wilshere came on but he failed to have an impact with little time left.
Lukas Podolski (On 71') - 6
Podolski didn't have many chances after coming on but he will be looking forward to next week's match against United if Wenger decides to give him a chance as a striker.
Thomas Vermaelen (On 90') - N/A