Pierre Kalulu's late effort saw Milan rescue a 2-2 draw for the second Serie A match running as Mattia Destro's double ultimately proved in vain for lowly Genoa.
The hosts, the last side to defeat the Rossoneri in Italy's top flight back in March, led twice as ex-Milan loanee Destro scored either side of Davide Calabria's excellent equaliser at the Luigi Ferraris.
But Kalulu tapped in from Alessio Romagnoli's downward header seven minutes from time to complete a breathless second half completely at odds with an insipid opening 45.
Leaders Milan fought back from a two-goal deficit to draw 2-2 at Parma last time out and are now 24 unbeaten in the league but only a point ahead of city rivals Inter. Genoa remain in the bottom three.