Houston overcame an early 12-point deficit, took a 12-point lead into the fourth period and fought off a Utah comeback bid.
The Jazz closed within 94-89 with 3:26 to play, but McGrady hit a jumper and two free throws, after which Yao Ming made a short hook shot to end the threat.
Mike James added 15 points for Houston, which began its season with a win over the Los Angeles Lakers. Yao had 11 points and seven rebounds.
McGrady scored 26 points in the first half as Houston took a 57-49 lead at intermission.
Utah defeated Houston over a seven-game series in the opening round of the playoffs last season.