Thaddeus Young added 27 points and 14 rebounds while Spencer Hawes and Lavoy Allen had 12 apiece for the Sixers.
Ed Davis had 18 points and 10 rebounds for the Raptors. Terrence Ross and Alan Anderson each scored 18.
Jose Calderon chipped in 13 points and Kyle Lowry had 11 points and 11 assists before fouling out for Toronto, which fell to 4-17 on the road. The Raptors lost their fourth in a row.
Despite a depleted lineup, the Raptors led virtually the whole game and by as many as 19 in the second half.
Toronto was missing forwards Andrea Bargnani (torn right elbow ligament) and Linas Kleiza (sore right knee), along with center Jonas Valanciunas (broken right ring finger).
While the Sixers erased the 19-point advantage and briefly took a 74-73 lead early in the fourth quarter, Toronto responded with a 15-4 run to go back ahead 88-78.
When the 76ers made another late surge to get to 92-90 on Young's dunk with 2:54 remaining, the Raptors countered with a jumper by Davis for a four-point lead with 2:09 left.
Young's dunk with 10.6 seconds left pulled the Sixers to 94-92.
Anderson converted a pair of free throws with 8.8 seconds to go for a 96-92 lead.
But it wasn't over.
A basket by Hawes cut it to 96-94 with 5 seconds left, and a turnover by Calderon gave the Sixers one last chance.
Holiday delivered with a tough drive and layup with 1.1 seconds left to force overtime.
In the extra session, Holiday completely took over and showed why he appears worthy of his first All-Star selection.
Holiday hit a pair of jumpers followed by a 3-pointer and a layup for a 105-99 lead.
The Raptors led by as many as 17 points in the first half and cruised to a 60-43 advantage heading into the locker room thanks to 59 percent shooting (24 of 41).