Houston opened strong in the third quarter with James Harden and James Ennis III making back-to-back three-pointers for a 72-62 lead, the biggest of the game.
LeBron James answered with a long-range shot of his own. He had another three-pointer rattle out moments later, but Rajon Rondo hustled into the lane to steal the rebound and lay it in while still in the air to cut the deficit to 72-68 with 10:41 left in the third quarter.
Rockets center Clint Capela converted a three-point play to stretch the lead to seven after a JaVale McGee foul. McGee, though, answered with a turnaround jumper of his own.