Martin connected on four 3-pointers and dished off seven assists while Luis Scola added 25 points and hauled down eight rebounds for Houston, which notched a second straight win.
The Rockets grabbed control of the contest with a 13-0 run in the third period, capped by Martin's lay-in with 6:35 left in the frame for a 71-56 Houston advantage.
Anthony's 3-pointer with 20 seconds left pulled the Nuggets to within four points at 105-101, but Denver could get no closer and lost to Houston for the second time in six meetings.
Anthony, meanwhile, tied a career high with his 50-point performance. The Nuggets forward went 16-of-24 from the field and 16-of-18 from the free-throw line and grabbed 11 rebounds for the game.