DeRozan looked to get his teammates involved in the first half but once Kyle Lowry left with a knee injury, the new All-Star took matters into his own hands with nine points in the fourth quarter to quell a Jazz comeback. The Raptors scored 13 of the game's final 16 points.
Valanciunas and Amir Johnson, who had 11 points and 11 rebounds, exposed the Jazz interior defense without Derrick Favors (hip).
Marvin Williams scored 23 points and Alec Burks had 20 off the bench but it wasn't enough to keep the Jazz from their third straight loss, their worst span since a four-game skid from Dec. 4-9.
Greivis Vasquez, who had 12 points, opened the fourth quarter with a floater to give the Raptors a 73-62 lead.
Burks made back-to-back driving layups to power an 8-0 run to get the Jazz within four points for the first time since early in the second quarter. But the Raptors used their own 11-2 surge to clinch the victory. DeRozan had seven straight for the Raptors in the stretch.
The Raptors had dropped seven of eight at Utah by an average of 14.9 points, but controlled this one almost all the way. Toronto's only win here since 2006 had been a 111-106 double-overtime victory on Jan. 25, 2012.
DeRozan has been effective no matter where he plays, but especially in games in the States, averaging 27 points over his last seven on the road.
Valanciunas also continued his upward trend with another strong game on the interior, with four offensive rebounds and many more plays where he kept the ball alive for Johnson.
The Jazz hoped to awaken Gordon Hayward and Trey Burke from their slumps but the pair, which has been shooting less than 30 percent, combined to make just 7 of 25 shots and commit seven turnovers.
Lowry had two points on 1-of-8 shooting before leaving to the locker room for good in the third quarter with right knee pain. He will be evaluated on Tuesday to see if he can play either of the final two games of this five-game Western Conference road trip.
The Raptors (14-12) have as many road wins as any team in the Eastern Conference, tied with Miami and Indiana. They have never finished a season above .500 away from home.
Favors' injured hip prevented him from playing and without their starting center, the Jazz have lost all six contests this year.
Enes Kanter had 10 points for Utah but was pulled after missing a defensive assignment and played just 20 minutes. The Jazz are 1-21 with the big man from Turkey in the starting lineup.
Notes: The Raptors are 18-10 after the seven-player trade with Sacramento on Dec. 7. . Toronto used a 31-17 second quarter to take control of the game. . DeRozan and Valanciunas were both poked in the eye during the course of the game. . The Jazz were 3 of 17 from behind the 3-point line. . Jeremy Evans missed the game for Utah with a bruised tailbone and elbow.