Chelsea had led in the shoot-out after Cristiano Ronaldo missed his spot-kick, but John Terry fired wide before Edwin van der Sar saved Nicolas Anelka's effort.
It was an amazing end to a scintillating game that had ended 1-1 after extra-time as Moscow hosted the first all-English Champions League Final between the two teams that have dominated the Premier League in the last four years.
In a cagey opening Chelsea created the first opening in the fourth minute when Florent Malouda did well to whip in a dangerous cross that Nemanja Vidic was forced to head clear.
Owen Hargreaves' mis-hit cross then almost caught Petr Cech out only for the keeper to recover his composure and make the save.
In the 17th minute Ronaldo beat Michael Essien easily, raced to the byline and fired in a cross that was just too high for Hargreaves.
United took a deserved lead in the 26th minute. Paul Scholes and Wes Brown combined well with the latter sending over a pin-point cross for the unmarked Ronaldo to plant a header past the stranded Petr Cech - the 42nd goal of an amazing season for the Portugal international.
It was excellent play by Brown and Ronaldo, but Essien was badly at fault with his positioning.
The goal immediately led to the game opening up and, in the 34th minute, Chelsea almost equalised when Frank Lampard found Didier Drogba who headed the ball into the danger area where Edwin van der Sar was forced to make a smart save to deny Michael Ballack.
United then launched a devastating counter-attack with Wayne Rooney and Ronaldo breaking at pace. Cech did superbly to keep Carlos Tevez's close-range effort out and then produced an outstanding save to stop Michael Carrick's follow-up shot.
United should have doubled their lead when Rooney sent a low cross into the penalty area that Claude Makelele missed but the surprised Tevez could not turn the ball into the net.
It proved to be a costly miss as, on the stroke of half-time, Essien's speculative long-range effort took two deflections before finding Lampard who rifled the ball past van der Sar who slipped at the vital moment.
The second half was dominated by Chelsea although, in the 54th minute, Ronaldo did superbly to find some space for Patrice Evra but the Frenchman over-hit his cross and a good chance was wasted.
When Chelsea hit back, Essien did the hard work by creating a shooting opportunity for himself, only to then fire his shot over the bar.
With 12 minutes of normal time left, out of nothing, Drogba tried his luck with a curling 25-yard effort that beat van der Sar only to come back into play off a post.
Four minutes into extra-time, Chelsea were denied by the woodwork again as Lampard hit the post after being set up by Ballack.
United almost grabbed the winner when Evra pulled the ball back for Ryan Giggs who seemed certain to score only for Terry to head the veteran Welshman's mis-hit shot away for a corner.
In a feisty finale Drogba was sent off for stupidly flicking his hand in to Vidic's face but Chelsea hung on to force the shoot-out, only to eventually lose in unbelievable fashion.