Schaub's four-yard pass to Andre Jobnson late in the second quarter put the Texans (1-0) up 24-0.
Jacoby Jones returned a punt 79 yards for a score less than a minute before halftime while Ben Tate, subbing for the injured Arian Foster, amassed 116 yards on 24 carries, including a two-yard first-quarter TD run.
Indianapolis (0-1) looked overmatched as it played without quarterback Peyton Manning for the first time in 227 games. The signal-caller is still recovering from off-season neck surgery.
Veteran Kerry Collins started in Manning's place and went 16-of-31 for 197 yards with one TD. The 38-year-old was sacked three times in the loss.
Reggie Wayne made seven grabs for 106 yards and a fourth-quarter score for the Colts.