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.
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 last 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.
What does it mean? Milan need Ibra boost
Zlatan Ibrahimovic has not featured for Milan since injuring his hamstring in the 3-1 win over Napoli on November 22. A couple of 2-2 draws have seen the Rossoneri's title tilt stall and Pioli will want his veteran Swedish striker, who returned to training this week, back in the fold as soon as possible.
Mattia the Best-ro for unlucky Genoa
The disappointing thing for Milan is Genoa had lost their past five home league matches – a club worst run. Destro, who had an unsuccessful temporary spell with Milan in 2015, scored with both his efforts on target, Genoa had four on target in total.
Kalulu keeps his cool… eventually
Kalulu will feel he may have scored on the stroke half-time but he stepped up when it mattered. The centre-back also made a tackle, had a game-high five interceptions and regained possession seven times for his team.
Key Opta Facts: Destro's first double for three years
- Milan have scored at least two goals in 14 consecutive games: a record in Serie A history, overtaking Torino 1948 (13).
- The Rossoneri are unbeaten in their last 24 league games: their longest run since 1993.
- Since the last May, among the teams in the top-five European leagues with at least 20 games during the period, only Milan (24) and Bayern Munich (21) have always scored.
- Destro scored twice in a Serie A game for the first time since December 2017, with Bologna.
Milan will not have an easy task as they look to get back to winning ways when they visit high-flying Sassuolo on Sunday, the same day Genoa go to fellow strugglers Benevento.