The Raptors snapped an 11-game skid on the road, winning away from home for the first time since Nov. 13 when they beat Indiana.
Toronto, which is 2-14 on the road, has also won three in a row for the first time this season.
Alan Anderson hit three 3-pointers in the fourth quarter and finished with 18 points.
Amir Johnson scored 17 points and DeMar DeRozan added 16.
Kyrie Irving, coming off a career-high 41 points Saturday, scored 23 points for Cleveland.
The reigning rookie of the year, currently playing with a broken bone in his jaw, is wearing a protective mask.