Alberto Gilardino equalised Kaka's early opener before the former Manchester City man spurned the chance to put his side ahead as the hosts laboured against the 10-man visitors
Kaka put the hosts ahead at the San Siro after four minutes, before former Milan striker Alberto Gilardino equalised from the spot.
Genoa had Thomas Manfredini dismissed for a tug on Mario Balotelli nine minutes from the break, but the striker failed to take advantage with the resulting penalty as his tame effort was saved.
Milan have not tasted victory in Serie A since October 19, while Genoa are now unbeaten in four.
Balotelli returned to Milan’s attack after a suspension, with Daniele Bonera making his first appearance of the season, replacing Philippe Mexes, who was injured in the warm-up. The visitors brought Mario Sampirisi and Davide Biondini in for Juraj Kucka and Isaac Cofie.
Sulley Muntari had the opening chance of the match for Milan after just three minutes, forcing Genoa goalkeeper Mattia Perin to unconvincingly fumble the ball wide from distance.
And the hosts were ahead a minute later when Kaka brought the ball down superbly form a pin-point Nigel de Jong pass before slotting under Perin from eight yards.
But Genoa were handed the opportunity to level matters after eight minutes when Urby Emanuelson carelessly tripped Sime Vrsaljko in his own area to concede a penalty.
Former Milan striker Gilardino made no mistake with the spot, firing it straight down the middle as Christian Abbiati dived to his right.
Balotelli attempted a spectacular effort midway through the half, controlling the ball with his chest before firing an overhead kick straight at Perin, and the former Manchester City striker looked dangerous throughout the opening 45 minutes.
Genoa's Thomas Manfredini was given his marching orders for hauling the 23-year-old to the ground in the penalty area after 36 minutes, but Balotelli was left red-faced as Perin outfoxed him to save his effort down the middle.
The miss was Balotelli's second in his career from 12 yards, although both have come this season.
Milan adopted a patient style of play at the beginning of the second half, but clear-cut chances were few and far between before De Jong fired straight at Perin from 20 yards after 58 minutes.
As the hosts began to turn the screw, Milan drew two superb saves from Perin – the first a tip over the crossbar from an Alessandro Matri header and the second low dive to his right to deny Kaka.
Genoa were riding out the storm, but only just. Valter Birsa had an effort tipped around the post by Perin 10 minutes from time, before Kaka fired an effort narrowly over the crossbar.
With time rapidly running out, Birsa headed agonisingly wide of the target and Cristian Zapata scuffed wide as Genoa clung on for a hard-fought point.