Pulisic was a second-half substitute in Turin and turned the game on its head having entered the fray afer 67 minutes.
Milan go above Napoli on goal difference and head to eighth-placed Sassuolo next Sunday.
Nikola Vlasic and Duvan Zapata had claimed an early advantage for the home side, who are now 16th looking for a first win since October 26.
Pulisic, 27, was named on the bench after suffering from flu symptoms, with Milan boss Max Allegri sitting out a touchline ban.
"I've been ill for the last few days, but I'm feeling a bit better today," Pulisic told DAZN.
"The most important thing isn't my goals, it's that we won the match."
The hosts raced to an early lead as Vlasic converted from the penalty spot and Zapata made it 2-0 after 17 minutes.
Seven minutes later Rabiot halved the deficit with a sublime effort from more than 25 metres out.
With 34 minutes to play Milan's Ruben Loftus-Cheek had a superb chance to equalise but Torino goalkeeper Franco Israel stopped the Englishman's impressive head.
Pulisic then entered the fray and made an immediate impact netting with his first touch from short range.
The 82-time international completed the comeback with 13 minutes left with a superb low half-volley.
During injury-time Pulisic was denied his hat-trick, and his eighth goal of the campaign but Christopher Nkunku was judged to be offside.
It was enough to send AC Milan to the top of the table although those early defence errors are a cause for concern.
"You can't start a match by conceding two goals so easily, we'll have to watch the video carefully and keep working," said Rabiot.
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