Ten-man Milan suffered their third defeat of the Serie A season as Genoa secured a 1-0 win at the Stadio Luigi Ferraris on Sunday.
Blerim Dzemaili's deflected free-kick put Genoa in front and Alessio Romagnoli's red card late in the first half gave Milan a mountain to climb.
Milan improved markedly in the second half, with Mario Balotelli looking especially dangerous in attack as he cleverly set up Luiz Adriano before going close with a shot of his own.
Balotelli - under the watching eyes of Italy head coach Antonio Conte - continued to threaten but Milan's push for a comeback ran out of steam as Genoa closed out the game.
The defeat leaves Sinisa Mihajlovic's men with nine points from their opening six matches, while Genoa claim just their second victory of the season.
Diego Capel's rasping drive from 25 yards had Diego Lopez scrambling early on as Milan struggled to retain possession against Genoa's high-energy 3-4-2-1 system.
And the home side took the lead with just 10 minutes on the clock, Dzemaili's fierce free-kick from distance clipping the top of the wall and flying beyond the helpless Lopez into the far corner.
Balotelli - awarded another start following his excellent display against Udinese - cut a frustrated figure early on, clipping a simple pass well into the stands before seeing a promising run halted by a petty foul.
Giacomo Bonaventura fired narrowly over from the edge of the area and Balotelli glanced a header just past the far post from the playmaker’s corner as Sinisa Mihajlovic’s side began to improve, but Milan's task was made all the more difficult just before the break when Romagnoli stuck an arm out to block Capel's run forward, earning himself a second yellow card.
Milan started the second half well, Luiz Adriano forcing a good low stop from Eugenio Lamanna after a clever run and pass from Balotelli, before Andrea Bertolacci tested the keeper following the Liverpool loanee's lay-off.
The Rossoneri were much improved despite the loss of a man and Balotelli forced another good stop from Lamanna when played in by Bertolacci, who then saw another effort blocked.
Genoa had threatened little in the second period but Olivier Ntcham wasted a good chance on the break, blasting the ball wide after Dzemaili's cut-back, before Capel cut inside and curled a left-footed drive just over.
Milan threw on Carlos Bacca as they continued to search for a late leveller and Juraj Kucka blazed over when set up by Luiz Adriano, but Gian Piero Gasperini's side saw out a much-needed victory against the tiring visitors.
