Valanciunas netted 18 overall for Toronto, which outscored the Cavaliers 37-21 in the third after trailing 44-39 at the break.
Terrence Ross provided 20 points with three steals and Kyle Lowry totaled 14 points, nine assists and six rebounds as the Raptors snapped Cleveland's six-game winning streak.
DeMar DeRozan helped out with 14 points.
The Cavs got 21 points with 11 rebounds from Luol Deng.
Kyrie Irving supplied 17 and nine assists.