Dragic, who started in place of ailing point guard Kyle Lowry, was one of seven Rockets in double figures. He also dished out eight assists.
New Jersey also played without its regular point guard, Deron Williams, who was out with a sore right calf. MarShon Brooks had 23 points and seven assists and Gerald Green led the Nets with 26 points off the bench.
Green's night ended on a sour noted when he inadvertently tipped a missed Houston shot into the New Jersey basket with 1:03 to play and the Nets on top 106-105. The bucket, which was credited to Luis Scola, sparked a seven-point Houston run that ended New Jersey's two-game winning streak.