Goran Dragic, who scored a career-high 35, missed a three-pointer at the buzzer that would have tied the game.
This was a game full of runs.
The Rockets jumped out to an 18-point lead in the second quarter, only to see the Suns storm back with a 29-8 run fueled by four Dragic triples in the period.
Phoenix then led by as much as 11 in the fourth before Houston closed on a 32-18 run.
Patrick Beverley was huge down the stretch, making big buckets, coming up with key defensive stops and bringing down crucial rebounds. He scored 20 points and tallied three steals.
The Suns made 11 threes and forced the Rockets into 22 turnovers, but they were outscored 64-42 in the paint. Houston also made 11 more free throws than Phoenix.
Gerald Green registered 23 points, 18 of that coming in the third quarter. Markieff Morris chipped in 21. Other than the trio of Dragic and those two, no other Suns player scored in double figures.
Houston shot 52.6 percent from the floor despite making only five of its 16 three-point tries. Phoenix hit on 48.8 percent of its shots.
With the victory, the Rockets earn a 2-1 season series win.