Terrence Jones scored 18 points and Isaiah Canaan put Houston ahead for good with a three-point play with 29 seconds left as the Rockets defeated the Phoenix Suns 95-92 on Monday night.
Phoenix had a chance to tie with 12 seconds left, but Archie Goodwin's 3-pointer missed, and Kostas Papanikolaou grabbed the rebound.
Houston was playing without Dwight Howard, who sat out for a second straight game with a bruised knee, and James Harden, who sat out with a bruised hip.
Canaan finished with 16 points while Troy Daniels added 12 points as the Rockets overcame 5 of 30 shooting from behind the arc and hitting 61 percent from the free throw line.
Eric Bledsoe had 13 points in 20 minutes, and Goran Dragic added 12 points in 18 minutes for the Suns.