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.
The Knicks were without G Raymond Felton (left hamstring) and G Iman Shumpert (right elbow). New York G Pablo Prigioni sat out with flulike symptoms. ... Knicks coach Mike Woodson said F Amare Stoudemire (left knee) and G J.R. Smith (left knee) both did individual workouts Monday and could take part in scrimmages Tuesday. ... Woodson said F Kenyon Martin (left ankle) might be able to practice Tuesday. Martin has not played this preseason. ... Toronto was without F Steve Novak (right thumb). ... Actor Isiah Whitlock Jr. attended the game.