Milan lose in shoot-out
With the score at 1-1 after 120 minutes, the lottery of penalties would be required to decide the champions.
The Italians booked their place in the final with a UEFA Champions League spot-kick victory over Juventus last season, but failed to recapture their success in Yokohama.
Dutch striker Jon Dahl Tomasson had given Milan a perfect start with the opening goal after 24 minutes, however Boca replied almost instantly to level the scores.
Matias Donnet was on hand just five minutes later to ensure the sides would go in all-square at the break in front of 66,757 partisan supporters.
After another 65 minutes of goalless action, including extra-time, it was the Argentines who held their nerve in the shoot-out to avenge their 2001 defeat to Bayern Munich.