The Mavericks had 30 points in the first period and 29 in the second, taking a 22 point lead into halftime. Cleveland managed just 14 points in the second quarter.
The Cavaliers had 60 points in the second half but it wasn't enough to erase the early deficit.
Cleveland's Kyrie Irving put up 27 shots, hitting 10, for a game-high 26 points. Anderson Varejao had 18 points and 21 rebounds, 17 of which came on the defensive end. Luol Deng marked his first game as a member of the Cavaliers with a 20-point effort.
Tristan Thompson, with 19 points and 10 rebounds, also had a double-double for Cleveland.