The experienced Spain international grabbed what proved to be the winning goal on 63 minutes, after the home team had twice drawn level in an enthralling battle in Milan.
The string-puller admitted that his team were not at their best during spells of the game, but highlighted the importance of beating the reigning Italian champions.
"We suffered a little in the first half, they attacked well and marked us well. It was a very entertaining game, full of chances. The victory gives us a lot of prestige and, in addition, it means we win the group," the 31-year-old told reporters after the game.
The midfielder was also keen to dedicate the victory to the club's assistant coach, Tito Vilanova, after the 42-year-old successfully underwent surgery on a parotid gland earlier in the day.
"This victory is dedicated to Tito [Vilanova] and his family. We have missed him," Xavi said after the final whistle.
Barcelona return to La Liga action on Saturday when they face an away trip to face Getafe.
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