DeRozan's masterclass saw Toronto end an 11-game losing streak in matches against the Bulls, which has included two losses already this season.
A stormy clash saw Chicago's Robin Lopez and Toronto's Serge Ibaka both ejected during the third quarter after a brawl erupted.
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Lopez finished the game with 12 points while Ibaka had 16 points before the dismissals.
"It felt great, in the fact that win, lose or draw, I felt we were scrapping, competing and that's all you can ask for from your team at this time of year," said Raptors coach Dwane Casey.
Lopez and Ibaka later played down the exchange of blows that led to their ejections.
"I think it was just a really physical game for everybody, it just kind of hit a flashpoint," said Lopez.
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"What happened is that he was playing physical basketball and he got frustrated," said Ibaka. "We started to push each other like always happens when there's contact and then he threw the punch. Like man I'm just going to defend myself."
The Bulls, who fell to 33-38, looked to be on course for an important victory after opening up a 15-point advantage at the close of the third quarter.
But the Raptors mounted a superb fourth quarter comeback with Cory Joseph cutting the lead to four points with two free throws with 3:27 left.
Fred VanVleet cut the lead to two points with a layup as the home crowd roared the Raptors on.
Toronto leveled it via a Joseph layup with 1:50 on the clock but Jimmy Butler hit back with a jumper and a layup to restore the Bulls' four-point cushion with 1:12 left.
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DeRozan then rescued Toronto with a jump shot that cut the lead to two points and tied it with a layup as the seconds ticked down.
The game went to overtime with the scores locked at 113-113 before DeRozan hit a jumper to help Toronto into a 117-115 lead.
A further layup by Patrick Patterson saw Toronto go four points clear with 44.7 left in overtime.
Butler's three-pointer set up a nervous finish with 2.8 seconds left but Toronto held on.
Butler finished with 37 points and 10 rebounds for Chicago. Rajon Rondo chipped in with 24 points for the Bulls while Paul Zipser had 12.
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