Olivier Giroud and Lukas Podolski had put the home side 2-0 up inside 23 minutes, but Fulham recovered with two goals from Dimitar Berbatov, either side of a Alex Kacaniklic header, and it took a second Giroud effort to rescue a point for Wenger's team.
Victory was denied the Gunners when Mark Schwarzer saved from Arteta in the final act of a dramatic game, but defeat would have been harsh on a spirited Fulham side.
It would have also deflected attention from another unconvincing display by Wenger's team, who let a two-goal lead slip for the second time in four days after the mid-week draw at Schalke in the Champions League.
The defensive weaknesses that have crept into Arsenal's play were once again plain to see, while Fulham confirmed the progress they have made under Martin Jol, with Berbatov again outstanding.
Wenger, though, can at least draw comfort from his side's comeback, two goals from Giroud, who has now scored four in four games, and another threatening display from Theo Walcott.
Walcott has found himself on the fringes of Wenger's plans while his contract situation remains unresolved, but he strengthened his case for the deal he wants by playing a role in both his side's opening goals on his first league start since August.
Fulham had started brightly and were arguably the dominant side before Walcott delivered a right-wing corner into the path of Giroud, who headed past away goalkeeper Mark Schwarzer in the 11th minute.
Then, when Podolski doubled Arsenal's lead 12 minutes later, it seemed the home side were on course to claim a comfortable victory.
Once again Walcott was involved, this time laying a neat flick into the path of Arteta, who picked out Podolski for the Germany international to stab the ball home from six yards.
The scoreline was harsh on Fulham, but they hit back through Berbatov, who was granted acres of space inside the Arsenal area to head home from Bryan Ruiz's corner.
Arsenal's attacking threat receded, while their defence continued to look shaky, and it was no surprise when Fulham levelled five minutes before half-time, with Berbatov again at the heart of the move.
The striker's run down the right flank was picked out by Fulham right-back Sascha Riether and Berbatov clipped a precise cross towards substitute Kacaniklic, who headed past Vito Mannone.
Giroud headed over immediately before the break but there was no doubt the momentum had swung Fulham's way.
The visitors were rewarded for their efforts mid-way through the second period when Arteta was dispossessed by Bryan Ruiz on the edge of his own box and fouled the Fulham forward as he tried to recover his mistake.
Referee Phil Dowd -- who had earlier resisted the temptation to show Fulham midfielder Steve Sidwell a second yellow card -- pointed to the spot and Berbatov beat Mannone with ease.
Arsenal looked a beaten side, but they rallied to draw level just four minutes later when Giroud and Walcott combined again.
Giroud fired a left-foot shot against the post but was presented with a second opportunity when Walcott collected the rebound and crossed for the striker to head home.
Arteta's late opportunity came when Riether was adjudged to have handled Andrey Arshavin's cross, but the Spaniard's penalty drew a fine stop from Schwarzer.
Source: AFP
Source: AFP