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 games unbeaten in the league but only a point ahead of city rivals Inter. Genoa remain in the bottom three.
Samu Castillejo curled wide of the far post and Hakan Calhanoglu's low free-kick tested Mattia Perin in an otherwise lacklustre opening.
Destro dragged just past the left upright after 37 minutes, prior to Ante Rebic showing a great piece of skill to beat Paolo Ghiglione only to shoot straight at Perin.
Kalulu put a point-blank header over from the resulting corner and Milan were punished two minutes after the break.
Gianluigi Donnarumma made a superb stop from Eldor Shomurodov's shot on the turn but Destro reacted quickest to tap in the rebound.
The lead lasted only five minutes as Calabria executed a superb daisy-cutter across goal from 25 yards to find the bottom-left corner.
Destro again proved Milan's scourge on the hour, though, when his downward header from Ghiglione's right-wing centre bounced off the ground and into the left side of the goal.
Substitute Jens Petter Hauge narrowly failed to pick out the bottom corner but shortly after Kalulu pounced on Romagnoli's knockdown to level proceedings again.
There was still time for Donnarumma to expertly parry away Gianluca Scamacca's audacious acrobatic effort as Stefano Pioli's table-toppers fought to another point.