Garrett Wilson had two of the scores with one-handed grabs as the Jets won for the first time under interim head coach Jeff Ulbrich.
Rodgers had thrown for just 32 yards in the first quarter, his career-low total of at least 10 attempts, while Jets rookie Malachi Corley missed a golden opportunity to open the scoring.
It appeared he grabbed his first NFL score at the end of an 18-yard run, but replays showed he dropped the ball in celebration before crossing the goal line.
The AFC South-leading Texans finally broke the deadlock just before halftime when Joe Mixon booted a three-yard field goal.
Wilson’s first one-handed touchdown catch tied the score in the third quarter, Ka’imi Fairbairn’s 54-yard field goal put the Texans back in front.
But early in the fourth quarter, Wilson added his second of the quarter with a spectacular effort at the end of Rodgers’ 26-yard pass on third-and-19, a replay that overturned the initial ruling of an incomplete pass.
Rodgers found Davante Adams with just under three minutes left, and though Fairbairn — who missed two earlier field goals — cut the deficit to 21-13 with 39 seconds left, the Jets recovered the onside kick to end the rout. you are a series.
Rodgers finished with 211 yards, C.J. Stroud went 11 of 30 for 191 yards for the Texans.