After starting slowly, the Texans translated four consecutive Miami turnovers in the final 6 1/2 minutes of the half into 24 points. Three of the turnovers were interceptions tossed by Dolphins rookie quarterback Ryan Tannehill.
Foster overcame a sore knee to rack up 79 yards and two scores on 26 carries as Houston (1-0) rolled in its opener.
Matt Schaub completed 20-of-31 passes for 266 yards with a touchdown in the victory.
Tannehill, chosen by Miami with the eighth overall NFL Draft pick in April, finished with 219 yards on 20-of-36 efficiency.
The Dolphins (0-1) lost in the debut of new head Coach Joe Philbin.