The Texans improved to 5-0, matching the Atlanta Falcons as the competition's only undefeated teams, while the Jets fell to 2-3, joining Buffalo and Miami one game behind AFC East division-leader New England.
Matt Schaub opened the scoring with a 34-yard touchdown pass to Owen Daniels 3:55 into the game but the Jets answered 6:58 later when Mark Sanchez connected with Jeff Cumberland on a 27-yard touchdown pass.
The Texans took a 14-7 lead early in the second quarter when Foster reached the end zone on a 13-yard run.
Houston's Shayne Graham kicked a 27-yard field goal on the last play of the second quarter to give the Texans a 17-7 half-time lead, then added a 42-yarder in the third quarter to put the visitors ahead 20-7.
On the ensuing kickoff, Jets' kick returner Joe McKnight carried the ball back 100 yards for a New York touchdown, trimming Houston's lead to 20-14.
Graham added a 22-yard field goal 13 seconds before the end of the third quarter to give the Texans a 23-14 advantage but Nick Folk kicked a 21-yard field goal for the Jets to lift New York within 23-17 with 11:55 remaining.
The Jets made a late push for a winning touchdown but a deflected Mark Sanchez pass was intercepted by Houston cornerback Kareem Jackson with 1:51 remaining to seal New York's fate.