Xavi's goal near the hour mark assured the Catalan club of the top spot in Group H after Zlatan Ibrahimovic and Boateng had cancelled out a Mark van Bommel own goal and a Lionel Messi strike.
After the match, the Ghanaian praised his side's display and stated they were unlucky not to get a better a result against the Champions League holders.
"We had a great match today, we played well," Boateng told Sky Sport Italia. "Barcelona are a great team, but we were unfortunate.
"However, the most important thing was to qualify for the knockout stages.
"Pep Guardiola's side are the best in the world, but today it was seen that we are also very strong when we are focused."
Milan will visit Viktoria Plzen in their last Champions League group match, while Barcelona will host BATE Borisov.
Starting last Friday and continuing every Friday through to January, Goal.com will publish extracts from Graham Hunter's highly-anticipated book, Barca: The Making of the Greatest Team in the World, which kicked off with a fascinating segment on Lionel Messi's rise to the top at Camp Nou. Don't miss it!