Moats, taking over after starter Steve Slaton lost yet another fumble, scored three touchdowns on consecutive fourth-quarter drives to help the Texans (5-3) win their third straight game for their best start in franchise history. Matt Schaub bounced back from two first-half interceptions to lead six scoring drives on seven possessions.
The Bills (3-5) were undone by an offense that managed 204 yards and nine first downs, with only three coming in the second half.
Buffalo squandered another opportunistic performance by its defense, which forced three turnovers, including two interceptions by rookie safety Jairus Byrd. The second-round pick out of Oregon became the first player since San Francisco's Dave Baker in 1960 to have two or more interceptions in three straight games.
The Bills' inability to muster any threat — both scoring drives came on short fields — eventually wore down the defense. Terrell Owens scored on a 29-yard run set up by Byrd's first interception. Rian Lindell hit a 21-yard field goal set up by Fred Jackson's 71-yard kickoff return late in the second quarter.
It didn't help that Buffalo got little pressure on Schaub after defensive end Aaron Schobel left with a groin injury.
Down 7-3 early in the second quarter, the Texans gained momentum once they stopped turning the ball over after three giveaways on their first four possessions.
Houston went ahead 17-10 early in the fourth quarter when Moats scored on an 11-yard run to cap a 10-play, 72-yard drive. The Texans went up 17-10 after Schaub hit Andre Johnson for a 2-point conversion.
The Texans scored on their next possession after they weren't fooled by the Bills' fake punt on a fourth-and-2 at the Buffalo 40. Moats scored on a 1-yard plunge and then scored again on a 3-yard run with 3:34 left.
Moats finished with a career-high 23 carries for 126 yards in place of Slaton, who lost a fumble on the Texans' third possession when Paul Posluszny punched the ball out of his hand following a 7-yard reception. Slaton has fumbled seven times this season and lost five.
Schaub went 25 of 34 for 268 yards and two interceptions in helping the Texans gain 439 yards. It was the fourth 400-yard game for the Texans this season to match a franchise best set last year.
Ryan Fitzpatrick, getting his second straight start in place of injured Trent Edwards (concussion), finished 15 of 23 for 117 yards, and two interceptions. Owens had five catches for 39 yards, plus his 29-yard touchdown run.
The Texans also overcame the loss of tight end Owen Daniels, who sprained his right knee in the first quarter.
Byrd's first interception came on Houston's first possession. He made a diving catch of Schaub's pass over the middle for Daniels, giving Buffalo the ball on its 13. The second came when Schaub's pass to Johnson over the middle bounced off the receiver's hands and directly to Byrd.
Byrd has interceptions in four straight games to give him seven on the season.