"You got to give yourself a chance to win and we did that tonight," Sanchez said.
The Texans (5-0) joined the Atlanta Falcons as the NFL's only teams without a loss.
"Arian stepped up and played huge," quarterback Matt Schaub said. "We're very excited to be 5-0 and get a win on the road."
The Jets (2-3) were heavy underdogs after coming off a 34-0 loss to San Francisco last week, but made a game of it. Backup quarterback Tim Tebow got the crowd fired up at times throughout the game, including running for a first down on a fake punt, but had little impact otherwise.
Houston also overcame a 100-yard kickoff return by Joe McKnight that cut the Jets' deficit to 20-14.
Schaub was 14 of 28 for 209 yards and a touchdown to Owen Daniels, winning his ninth straight game the longest active streak in the NFL dating to last season. Daniels finished with four catches for 79 yards for the Texans, who have just their second five-game winning streak in team history.
"It's definitely our best start," Daniels said, "and a big part of that is it doesn't matter on this team about stats or individually what is going on. It's great to be a part of something like that."
The enthusiasm was tempered, though, by a left knee injury to star linebacker Brian Cushing that coach Gary Kubiak said he was "very concerned" about.
"I don't know what happened," Kubiak said. "They tell me he cut on a play and his foot might have got stuck in the turf."
Nick Folk's 21-yard field goal with 11:55 left made it 23-17, but the Jets appeared as though they would get more.
"I honestly thought we were going to drive down the field and score a touchdown" on the last drive," wide receiver Chaz Schilens said. "It's not going the right way."
McKnight's 100-yard kickoff return the second of his career cut the Texans' lead to 20-14 with 4:38 left in the third quarter.