The hosts welcomed Brian Hoyer back to the side after he missed last week through concussion, and the quarterback wasted no time in marking his return with the opening score of the contest.
Hoyer completed seven of seven pass attempts on his side's opening possession, including a 10-yard pass to tight end Ryan Griffin to take into the endzone - the first time this season that the Texans have scored on their opening drive.
The Saints went into the match with the NFL's worst defence, and despite the decision to fire defensive coordinator Rob Ryan and replace him with Dennis Allen last week, there were no signs of immediate improvement as Houston quickly added a second touchdown.
This time it was Cecil Shorts III who got the score, connecting with Hoyer from three yards to double the hosts' advantage as the Texans quarterback went nine for nine in the first quarter.
The visitors did finally get on the board later in the second quarter when Kai Forbath kicked a 30-yard field goal, and he added a mammoth second from 57 yards towards the closing stages of the half to reduce the deficit to eight at the break.