Kris Humphries had 16 points and nine rebounds and Morris Peterson added 16 points for the Raptors, who are 6-0 in exhibition play.
Toronto won despite missing All-Star forward Chris Bosh (plantar fasciitis), No. 1 pick Andrea Bargnani (sore left ankle) and point guard T.J. Ford (sore left hamstring and back).
Bosh has missed three preseason games.
LeBron James scored 21 points in three quarters for the Cavaliers, who dropped to 2-5.
Jones signed with Toronto in the offseason and is expected to back up Anthony Parker, who hasn't played as well as Jones in the preseason.
The Raptors trailed by as many as 13 in the first half, but they began on the second half on a 15-4 run.
After Humphries grabbed an offensive rebound and made a layup to give Toronto a two-point lead with just under a minute left, Cleveland's Sasha Pavlovic made just one of two free throws with 30 seconds left.
After a timeout, Toronto looked confused and Jose Calderon missed badly with a running jumper, but Humphries grabbed the rebound to seal the victory.
Longtime Raptors fan Samuel L. Jackson sat courtside.