The winning boot came seconds after the Texans drove down the field and notched the game-tying touchdown. Deshaun Watson went deep down the sideline for DeAndre Hopkins to start the drive and went deep again on the score to Kenny Stills, who was making his Texans debut.
Houston initially missed the go-ahead extra point, but the Saints were penalized for roughing the kicker. Ka'imi Fairbairn made good on his second try to give the Texans a 28-27 advantage with 37 seconds left.
The Saints responded, though, with Drew Brees completing passes to Ted Ginn Jr., Michael Thomas, and Ginn again on the ensuing possession. Lutz, who missed a 56-yarder earlier in the game, then delivered the home team a 30-28 victory.
The win snapped a five-game losing streak for the Saints in season openers.
Brees threw for 370 yards with two touchdowns and an interception, while Alvin Kamara rushed for 97 yards on 13 carries. New Orleans trailed 14-3 at halftime and didn't take its first lead until early in the fourth quarter.
Watson tossed 268 yards, three touchdowns, and an interception, adding a score on the ground in the losing effort. His first two touchdown passes went to Hopkins.