Inter warmed up for the Champions League final with a 1-0 win over Torino to cap off their Serie A campaign.
The Nerazzurri head to Istanbul to face Manchester City on June 10, but the Coppa Italia winners had league business to attend to on Saturday.
Olivier Giroud's superb header saw Milan end a five-game winless streak in Serie A but Zlatan Ibrahimovic had to wait for his comeback in a 1-0 victory over Torino.
Milan, playing their 3,000th Serie A game, had lost their last four matches in all competitions heading into Friday's tussle at San Siro but they came away with the points thanks to Giroud's moment of quality.
Torino stunned Milan to reach the Coppa Italia quarter-finals with a remarkable extra-time win at San Siro on Wednesday, Michel Adopo scoring the only goal to fire the 10-man visitors through.
A much-changed Milan side produced a disjointed display, struggling to break Torino down even after Koffi Djidji received his second booking with 20 minutes remaining in normal time.
Milan failed to move back within three points of Serie A leaders Napoli as goals from Koffi Djidji and Aleksey Miranchuk condemned the Rossoneri to a surprise 2-1 loss to Torino.
Miranchuk followed up Djidji's glancing header with a cultured left-footed finish as Torino scored twice in two frantic first-half minutes to stun Milan at the Stadio Olimpico Grande Torino.
Dusan Vlahovic scored the only goal of the game as Juventus lifted the gloom with a 1-0 Derby della Mole win at Torino.
Head coach Massimiliano Allegri has come under increasing pressure following 2-0 defeats to Milan and Maccabi Haifa, but the Bianconeri secured only their fourth Serie A win of the season against their city rivals on Saturday.
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