Rudy Gay scored 19 points, Kyle Lowry had 11 and Tyler Hansborough 10 as the Raptors improved to 5-1 in the preseason.
Beno Udrih scored 19 points and Metta World Peace had 16 for the Knicks, who lost for the third time in four games. Tyson Chandler and Tim Hardaway Jr. each scored 15.
Andrea Bargnani had 13 against his former team, while Carmelo Anthony had nine points and eight rebounds in 26 minutes.
A pair of 3-pointers by Ross gave the Raptors a 110-103 edge with 2:22 left in the first overtime, but New York responded with an 10-0 run, taking the lead on Udrih's 3 with 37 seconds left, then adding two more on a pair of free throws by Hardaway Jr.
After missing a 3 with 6 seconds left, Ross sent it to double overtime with a buzzer-beating 3 from the wing.
Toronto's Dwight Buycks scored the first two baskets of the second overtime and Ross added a third, giving the Raptors a six-point cushion.
Ross sealed it with four made free throws in the final six seconds.
World Peace picked up a technical foul with 5:22 left in the fourth following an altercation with Hansborough.