Torino's Andrea Belotti and Marco Benassi put the home side on top after 26 minutes but Milan got back on level terms by the hour mark through Andrea Bertolacci and a Carlos Bacca penalty.
Milan moved up to fifth with 37 points, eight behind leaders Juventus, who have a game in hand, while Torino are ninth.
Milan defender Gabriel Paletta set the tone for a chaotic night in the second minute when his misplaced clearance hit Torino's Joel Obi on the head but rebounded wide of the goal.
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Torino went ahead after 21 minutes when Belotti turned in Adem Ljajic's miskicked shot for his 14th league goal of the season and Benassi added a second for the hosts five minutes later following a penalty area scramble.
Milan were in complete disarray and conceded a penalty when Ignazio Abate brought down Antonio Barreca in the 32nd minute.
But teenage keeper Gianluigi Donnarumma, who saved a penalty in Milan's 3-2 win over Torino earlier in the season, blocked Ljajic's spot kick and Iago Falque blasted the rebound over.
Milan scored twice in five minutes after the interval, Bertolacci scrambling the ball home in the 55th minute before Colombia forward Bacca converted a penalty on the hour.
There was still time for Milan defender Alessio Romagnoli to be sent off for a second bookable offence in the 89th before they missed two golden chances to grab a winner on the break.
(Writing by Brian Homewood; Editing by Ken Ferris)
