United twice took the lead. First through a Gallas own goal which was cancelled out by Francesc Fabregas's 11th of the season.
Cristiano Ronaldo made it 2-1 with just nine minutes left, but Gallas made amends for turning into his own net with just seconds remaining.
Arsenal were resilient and determined and largely controlled possession, but faced a Sir Alex Ferguson side who counter-attacked efficiently to ensure the result was in the balance until the final kick.
The game got off to a tense start. The first real opportunity fell to Emmanuel Adebayor after ten minutes when his header from Alex Hleb's cross fell disappointingly wide.
Manchester United's response was immediate when Carlos Tevez should have done better when put through by a clever ball over the top from Wayne Rooney.
While Emmanuel Eboue was caught ball watching, the close attentions of Kolo Toure were enough to force the Argentine to put the ball wide.
Ryan Giggs should have opened the scoring for United when the visitors broke away following a wasted Arsenal free-kick.
The ball was shifted swiftly to Ronaldo on the right flank and his cross found Giggs, who had made a run into the left side of the Arsenal area.
All that was needed was a touch, but the former Wales international got the ball caught in his feet and the ball bounced wide.
Arsenal's next free-kick was a better one. Again from the right and again delivered by Fabregas seemingly exactly as ordered by his captain William Gallas, who had delayed the kick to make his request.
Gallas made a run the near post to meet the ball and directed his header downwards and goalbound, but fortunately for United, Edwin Van der Sar was alert and saved with his feet.
With just seconds of the first half left on the clock, Manchester United took the lead.
Giggs burst down the right flank and the Gunners defence allowed the ball to find Rooney in the box.
The United striker got a touch to the ball but as his effort spooned up, Gallas, who was falling to the ground, appeared to redirect the ball past Manuel Almunia.
The Gunners made the perfect start to the second half when Fabregas levelled the scores on 48 minutes.
The midfielder netted for the 11th time this season after Eboue had initially slipped in Adebayor on the right side of the area.
Van der Sar bravely blocked the Togo striker's path, but the ball found its way to Fabregas waiting on the penalty spot and the young Spaniard drilled a shot into the bottom left corner of the net.
Wayne Rooney should have done better on 63 minutes when he met Giggs cross from the right but the United striker's shot flew well wide.
Ronaldo put United back in the lead on 82 minutes after a clever back heel on the right flank allowed Patrice Evra to run beyond the Arsenal rearguard.
Almunia came out too quickly and the left-back was able to pick out Ronaldo running into the box to place the ball into an unguarded net.
Evra almost turned into his own net three minutes later when a cross from the left flank eluded Adebayor and the French defender's attempted clearance shaved the top of his own bar.
Gallas levelled the scores and secured a point in injury-time when the eagle-eyed linesman spotted that the Arsenal captain's shot from an acute angle had crossed the line before Van der Sar patted it away.