The Patriots recovered a fumble on a kickoff, then rookie quarterback Jacoby Brissett took a bootleg 27 yards on first down for a touchdown and a 10-0 lead on the Texans late in the first quarter.
Charles James had fumbled the kickoff after a Stephen Gostkowski field goal, and Duron Harmon recovered for the Patriots.
On the previous drive, Brissett hit rookie wide receiver Malcolm Mitchell on a 27-yard gain to the Texans 15-yard line but the Patriots ended up settling for a field goal on fourth and one at the 6-yard line.
Brissett has hit 4-of-6 passes for 43 yards. The field goal drive covered 74 yards in 10 plays.