Carl Landry scored 15 points and Chuck Hayes had eight points and eight rebounds for the Rockets (4-3).
Kevin Durant scored 20 points in 26 minutes before sitting out the fourth quarter for the Thunder (2-3).
The Rockets led by one at halftime and built a 14-point lead when Oklahoma City missed 15 of 19 shots and had five turnovers in the third quarter.
Ariza drove for two layups and hit a 3-pointer during an 18-5 run that put Houston ahead 79-65. Ariza scored 10 points and Hayes grabbed five rebounds in the decisive third.
Shane Battier joined four Houston reserves for the start of the final quarter and the Rockets maintained a comfortable lead.
Pops Mensah-Bonsu, vying for a spot on the opening day roster, finished two fast breaks with dunks off passes from Budinger to push the lead to 96-77 with about 5 minutes left. Mensah-Bonsu finished with 13 points.
The Rockets shot 51 percent from the field for the game and held the Thunder to 33 second-half points.
Durant hit his first four shots, and his 3-pointer with 3:14 left in the opening quarter gave the Thunder their first lead, 22-20.
Durant scored 12 points in the first quarter, but Battier had 11 and the teams were tied at 33.
The Rockets led 53-52 at halftime even after Oklahoma City shot 57 percent from the field (21 of 37). Houston went 7 of 10 from 3-point range in the half.