Toronto guard Jose Calderon matched Holiday to knot the score with 42.9 seconds to go. Green and Raptors forward Chris Bosh then missed layups, and the fourth period ended, 114-114.
With the win, Toronto improved to 38-37. Entering the game, the Raptors were a game and a half up on the Chicago Bulls for the eighth and final Eastern Conference playoff berth. Chicago hosted the Charlotte Bobcats on Saturday night.
The Sixers (26-50) have six games remaining, beginning with one against visiting Detroit on Tuesday.
"We're going to fight," said Williams, who scored 12 points after he missed the team's previous five outings because of lower-back pain. "We still have games to play. We have not packed it in, obviously."
The Sixers received 33 points and 11 assists from Iguodala, both season highs. Holiday established a personal best with 25 points. For Toronto, Bosh (28) and center Andrea Bargnani (23) led the way.
Both squads shot well from the floor - the Sixers, 55.6 percent; Toronto, 56.3.
The Sixers trailed by three at intermission after accumulating 20 assists, their most in any half this season.
After a three-point basket from beyond half-court by Bargnani just before the third quarter ended, Toronto led by 10 points.
But when Holiday picked up a Toronto turnover, and worked his way downcourt and all the way to the hoop for a nasty lefthanded dunk, the Sixers were within 106-105 with a little more than five minutes remaining. A Green jumper with 3:03 to go gave the Sixers a 107-106 edge.
The contest was later tied at 109 with 2:21 left in regulation.
"We got some key stops, but we couldn't get a rebound," said Jordan, whose team was beaten, 42-27, on the boards.
Despite shooting 57.9 percent from the floor, and 42.9 percent from beyond the arc, the Sixers entered halftime down by 63-60. That was because they allowed Toronto to shoot 58.3 percent and 50.0 percent.
