Gallas turned Wayne Rooney's half-hit effort into his own goal on the stroke of half time to give United the lead.
Cesc Fabregas' cool finish put Arsenal level two minutes after the break, but Cristiano Ronaldo slid home Patrice Evra's cross nine minutes from time.
But Gallas then scrambled in Gael Clichy's cross to earn a point.
The opening 45 minutes proved an anti-climax until Gallas diverted Rooney's tame shot in on the stroke of half-time.
Arsenal had reasonable penalty claims ignored by referee Howard Webb after 15 minutes when Nemanja Vidic tugged Alexander Hleb's shirt as they tangled in the area.
United had a good chance seconds later when Bacary Sagna failed to react to Ronaldo's cross and Ryan Giggs, perhaps caught by surprise, could only turn a close-range effort wide.
Owen Hargreaves was outstanding in shielding United's defence from Arsenal's attacking threat, but he was powerless as the Gunners almost went ahead after after 35 minutes.
Gallas escaped the attentions of the United rearguard to glance Fabregas' free-kick against the legs of Edwin van der Sar.
United's Brazilian midfield man Anderson is clearly a talent, but he demonstrated an unsavoury side to his nature that predictably infuriated the crowd.
He flamboyantly demanded referee Webb show yellow cards to Arsenal players, then rolled in ridiculous fashion after a foul by Fabregas that earned the Spanish youngster a booking.
United staged a smash-and-grab in first-half stoppage time, Ronaldo crossing for Rooney, who failed to make a proper connection but saw Gallas provide a crucial deflection past Manuel Almunia.
The gauntlet was thrown down to Arsenal - but they picked it up to equalise two minutes after the restart.
Emmanuel Eboue played in Emmanuel Adebayor, who was blocked by Van der Sar, but Sagna crossed the loose ball for Fabregas to slide in a composed finish.
Arsenal had started to dominate possession, but it was United who had the next big chance after 63 minutes.
Giggs found Rooney in space in the area, but he headed wastefully wide when he should have at least worked keeper Almunia.
Both managers made changes in the final 15 minutes, Wenger sending on Theo Walcott for Eboue, while Ferguson replaced the subdued Carlos Tevez and Anderson with Louis Saha and Michael Carrick.
The changes worked better for United as they took a vital lead with nine minutes left.
Walcott failed to track Evra, and when Saha played him in he crossed perfectly for Ronaldo to score.
Evra then enjoyed a huge piece of luck when he sliced substitute Eduardo da Silva's cross against his own bar with Van der Sar helpless.
Arsenal pressed forward and got the draw they deserved when Clichy's cross sparked a goalmouth scramble which ended with a shot from Gallas which, even though Van der Sar clawed it out, had clearly crossed the line.