A first-half strike from Jens Petter Hauge sealed all three points for a much-altered Rossoneri, who fielded four players born after January 1, 2000 for the first time.
Despite making seven changes to the team that beat Celtic on matchday five, Stefano Pioli's men still made fairly light work of Sparta, who have now gone eight games without a win over Milan in European competition.
A red card for Dominik Plechaty left Sparta with too much to do, with Milan progressing as group winners after Lille's surprise defeat at Celtic.
Hauge opened the scoring in fine fashion 23 minutes in, nutmegging Tomas Wiesner before placing a precise low finish beyond the reach of goalkeeper Milan Heca.
Samu Castillejo was denied a second Milan goal by Heca shortly before the break as the Rossoneri sought to take control.
Sparta threatened little until David Moberg Karlsson's arrival 65 minutes in, the Swede producing a tantalising cross that just evaded the men in red shirts after a bamboozling run.
Once Plecharty was sent off with 13 minutes of normal time left for a poor challenge on Rafael Leao, the contest was effectively over, although Ciprian Tatarusanu had to make a fine one-handed stop to deny Karlsson an injury-time equaliser.