Weekend wins for title rivals Napoli and Inter left Milan in third and they knew three points were required to return to the summit on Monday.
However, they were 2-0 down after 17 minutes.
Nikola Vlasic gave the home side the lead with a penalty after nine minutes, and then made the second goal eight minutes later when he powered forward to feed Duvan Zapata, whose powerful angled drive beat Mike Maignan.
Milan got back into the game seven minutes later, Adrien Rabiot lashing in a shot from 35 metres that will feature in many goal of the season competitions come May.
It fell to American forward Pulisic to turn the game around with two second-half goals. After 67 minutes, one minute after replacing Davide Bartesaghi, he found himself unmarked in the box and made no mistake from close range.
Ten minutes later Pulisic put the visitors ahead for the first time when he swept home a low cross from the right.
Milan avoided what would have been only their second defeat of the season and extended their unbeaten league run to 13 games.
The result leaves Torino, a club with the worst defence in the league, in 16th place, one of four teams on 14 points.
Elsewhere, Genoa won a second consecutive league match for the first time in almost two years when a late goal from Brooke Norton-Cuffy secured a 2-1 victory at Udinese.
The 83rd-minute decider was the England U21 international's first goal for the club since signing from Arsenal last year.
The result lifted Genoa to 14th, while Udinese stay 11th.
At the bottom of the table, a penalty from Adrian Benedyczak gave Parma a 1-0 win at Pisa.
Injured Socceroos defender Adrian Circati (thigh) watched on as his Parma side moved four points clear of the relegation zone and left Pisa third bottom.
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