The Dutchman can expect to keep his job for the time being after Abdoulay Konko's own-goal ensured Alvaro Dominguez's second-half strike was not enough to condemn Milan to a fourth straight defeat.
Other results on Sunday meant the 18-time champions slumped to 12th in the table, where they lie 42 points behind leaders Juventus and 11 off the nearest Europa League place with nine games to play.
Lazio, meanwhile, remain in seventh place and five points off the European pace.
The Romans sensed their opponents' fear and trepidation from the first whistle and took the initiative, Antonio Candreva and Keita Balde Diao combining well to break into the box.
Neither man could get a decent shot away, and Diego Novaretti's header from a Candreva cross would not find the target.
Unperturbed, Lazio continued to pour forward and in the 35th minute Candreva let rip with a fierce shot from distance that deflected off a Milan player and went out.
It looked like the Biancocelesti had made the breakthrough their play deserved when Novaretti's header crossed the line four minutes before the break.
Visiting goalkeeper Marco Amelia made a hash of holding onto the ball when the Argentinian nodded the ball downwards.
It squirmed into the goal but referee Gianluca Rocchi ruled Giuseppe Biava had impeded Milan defender Philippe Mexes in the build-up and turned down Lazio's appeals.
Two minutes later, Milan raced up the other end and forced home an opening goal.
It was Kaka who did all the leg work, the tricky Brazilian weaving into the box from the left, but Konko contributed the fateful deflection that sent the ball beyond Etrit Berisha.
Lazio felt hard done by and set out to make amends for the unfortunate own goal when play resumed.
Candreva burst forward to test Amelia and Konko almost cancelled out his error with a low attempt on the rebound that Milan's keeper did well to smother.
In the 61st minute, Gonzalez dragged Lazio back into the game with a well-aimed header to the far corner from Lucas Biglia's cross.
The benched Mario Balotelli had since been introduced for Keisuke Honda but he could not make a winning impact, instead smashing the ball against the bottom of the post with his angled shot.
Giampaolo Pazzini's failure to convert Sulley Muntari's assist moments earlier was arguably more important to the final outcome but, at the full-time whistle, Milan had claimed their first point in a month.