Andrea Bertolacci opened the scoring at San Siro before M'Baye Niang netted against his former club and although Philippe Mexes pulled a goal back, Jeremy Menez was then dismissed
Ten-man AC Milan did nothing to halt the unrest surrounding the Serie A club as they suffered a 3-1 home defeat to Genoa.
Filippo Inzaghi's side went into Wednesday's game harbouring only slim hopes of a European place and with fans continuing to voice their disapproval at the €91.3m losses revealed by Milan the previous day.
Sections of the home support positioned themselves to spell out the word 'basta' - meaning 'enough' - but Milan's disappointing form on the field shows no signs of abating.
Indeed, Genoa dictated matters for the majority of the contest and took the lead through midfielder Andrea Bertolacci's solo goal.
Tino Costa's deflected close-range finish in the 48th minute put Genoa in control, only for a superb 66th-minute strike from Philippe Mexes to give Milan hope.
But any prospect of the hosts completing a fine comeback were put to bed when forward Jeremy Menez was sent off for a second bookable offence, and Iago Falque's injury-time penalty secured a first win for Genoa over Milan at San Siro for 57 years.
Genoa made a brilliant start, but spurned a host of early chances.
Bertolacci saw a low drive tipped around the post by Diego Lopez, who then denied Zakarya Bergdich with a near-post save following good link-up play with Milan loanee M'Baye Niang.
Niang was denied by a fine one-on-one stop from Lopez, with the Milan goalkeeper thwarting Bertolacci again after Milan had carelessly conceded possession.
But Bertolacci finally got his goal in the 37th minute as he was afforded the space to surge from midfield to the penalty area and cleverly evade an Adil Rami challenge before slotting the ball into the bottom-left corner.
Falque then went close to doubling Genoa's advantage, but his curling effort flew narrowly wide of the far post.
However, Falque atoned for that miss three minutes after the restart by teeing up Costa, whose shot deflected off Niang, to make it 2-0 at the end of an excellent Genoa counter-attack.
Milan mounted a response against the run of play, as Mexes lashed in off the underside of the crossbar following a well-worked short corner routine.
Yet Mexes' French compatriot Menez made Milan's task harder when he was given his marching orders six minutes later for a foul on Edenilson.
Lopez produced a fine double save to keep out efforts from Falque and Maxime Lestienne, but he could do nothing to prevent the Spaniard from powering a spot-kick into the net after an Ignazio Abate foul to send Genoa sixth in the table.