Irving tied it again with a layup but Calderon promptly answered with a layup at the other end, putting the Raptors up 98-96 with 12 seconds to go.
The Cavaliers then called timeout, and Scott urged Irving to go for it.
"I said, 'Me personally, I would go for the win,'" Scott said. "'Don't leave much time up there, just go for the win.' He said 'That's what I'm going do, sounds good.' Just great coaching, that's all that is."
"That's big time to say 'I'm going to do it,' and then go out there and do it like he did," Scott said. "I wasn't surprised. I was maybe giddy more than anything."
Irving's big 3 put him over 30 points for the third straight game.
"He's been everything that I've asked him to be, which is aggressive from start to finish," Scott said. "That's what we need from him."
DeRozan, whose buzzer-beating jump shot gave Toronto a 97-95 victory at Orlando on Thursday, got off to a strong start, making six of his first seven field-goal attempts and scoring 12 points to help the Raptors to a 25-19 lead after one. But DeRozan had just three points the rest of the way.
Irving scored eight points in the second and Speights added seven as Cleveland closed the gap, but an eight-point effort by Davis gave Toronto a 50-46 lead at the half.
NOTES: Cleveland's Daniel Gibson left at half with a sore right big toe and did not return. ... Toronto's Landry Fields started despite suffering from flu-like symptoms. ... Cavaliers rookie Tyler Zeller had 12 rebounds, two shy of his career high. ... Cleveland F Luke Walton did not play because of soreness in his left foot and ankle. ... The Raptors wore camouflage uniforms to mark Canadian Forces Appreciation Night. More than 500 Canadian Forces members and their families attended the game.