Wayne Rooney put United in front just before the break but Cesc Fabregas grabbed the equalizer shortly after the interval.
Cristiano Ronaldo restored the lead for the Red Devils eight minutes from time but Gallas' last-gasp effort ensured Arsenal are still on top of the Premiership.
Arsenal are in charge of the league table with 27 points and one game in hand, ahead of second-placed United on goal difference.
A free-flowing football was expected between the stylish teams but they instead deployed a cautious strategy in the first-half.
Arsenal players appealed for penalty after 15 minutes when United defender Nemanja Vidic tugged Alexander Hleb's shirt but the referee waved play on.
Television replays showed that there was a clear contact between Vidic and the Belarusian midfielder.
United had the first threat in the 17th minute when Ronaldo outpaced Mathieu Flamini before crossing at the far post but Ryan Giggs' slight touch missed the target.
Six minutes later, Giggs collected a loose ball before firing a left-footed shot that went over the bar.
In the 36th minute, Gallas outjumped Patrice Evra to head Fabregas' pinpoint free-kick but Edwin van der Sar blocked it by his legs.
Rooney continued his fine goalscoring run to silence the home crowd one minute into the first-half's additional time.
Portuguese winger Ronaldo raced down the right and sent a low cross at the near post to Rooney, whose simple shot deflected off Gallas' hands and went into the net.
In-form Spanish midfielder Fabregas drew Arsenal level three minutes after re-start.
Emmanuel Adebayor latched on to a through pass and went clear on goal but Van der Sar rushed out to deny the Togolese striker's effort.
The ball went to Bacary Sagna, who pulled back to Fabregas and the Spanish ace slotted home with two United players on the goal line.
United looked to have secured a precious win when Ronaldo restored their lead eight minutes from time.
Substitute Louis Saha threaded a superb pass through to the onrushing Evra, who squared to Ronaldo for an easy tap-in after keeper Manuel Almunia carelessly rushed outwards.
Gallas secured a share of spoils after a goal-mouth scramble when his close-range shot crossed the line before Van der Sar made a late attempt to clear it.