Jose Ignacio was the hero for Celta, after Kaka had given Milan the lead but for Jesuli to equalise soon after, as the home side paid for fielding an under-strength squad.
Rossoneri boss Carlo Ancelotti left seven regulars out of their final group match against Celta - with Paolo Maldini, Cafu, Alessandro Nesta, Andrei Shevchenko, Gennaro Gattuso, Andrea Pirlo and Giuseppe Pancaro all having left for Japan ahead of the Intercontinental Cup match versus Boca Juniors.
A half-empty San Siro saw an eventful start to the match, with very little to pick between both sides in the early stages.
Milan then started to offer more in terms of attacking qualities, with Serginho unlucky not to give the home side the lead with a fine curling free kick that beat Celta goalkeeper Pablo Cavallero but hit the bar while Clarence Seedorf forced a good save from Cavallero following a swerving point blank strike.
Then just before the break, both sides scored a goal, with Milan taking the lead with a fine strike from Kaka before Jesuli equalised two minutes later for Celta, as it was 1-1 at the break.
Celta offered little in the way of attack before they scored and Savo Milosevic nearly gave the Spanish side a half time lead but his close-range shot was well stopped by Christian Abbiati.
The visitors continued with their fine play in the second half and were unlucky not to score through Juanfran, as he hit the side-netting with a close-range shot.
Celta kept pressing forward with former Arsenal man Silvinho going close with a left-footed free kick while Jesuli nearly scored a second with a volley that went over the bar.
But Miguel Angel Lotina's men made the breakthrough as Peter Luccin's cross from the right found match-winner Jose Ignacio, who despite mis-hitting his first chance in front of goal, was able to finish with his second chance and give Celta a crucial 2-1 lead.
The visitors kept their shape towards the final stages and the final whistle brought delight to the Spanish side, who snatch second spot in Group H with the victory.
