A near-faultless performance from the Texans defense meant that a fourth-quarter DeAndre Hopkins touchdown was the difference as the Bengals slipped to 8-1.
Andy Dalton took opportunities to rush as often as possible early in the game, but with the Texans and Bengals both showing defensive resiliency, the opening score did not arrive until Mike Nugent's 42-yard field goal handed the home team the lead late in the first quarter.
Texans quarterback Brian Hoyer led his offense to the one-yard line as the visitors started to find their rhythm, before settling for making it 3-3 when Nick Novak converted a field goal from 22 yards.
Nugent hit back with another effort of his own, this time from 39 yards, as the first half came to an end with both sides still searching for their best in possession of the ball.
Dalton continued to struggle in a scoreless third quarter, with Jonathan Joseph intercepting a pass as the impressive Texans defense ensured the Cincinnati crowd remained frustrated for most of the night.
Houston were forced into a change when Hoyer was taken off to be evaluated for a possible concussion, which handed an opportunity to TJ Yates, who delivered the goods early in the fourth quarter as Hopkins claimed a 22-yard pass with one hand on the stretch in the endzone.
It proved to be a vital moment in the game as Houston continued to limit the options on offer to Dalton as the visiting defense made it 10 consecutive quarters without giving up a touchdown to their opponents.
After being sacked by JJ Watt late in the game, Dalton and his teammates appeared to be finished before the quarterback led his side into Houston territory for the first time in the second half just prior to the two-minute warning.
However, Quentin Demps recovered a fumble on fourth down after AJ Green had failed to bring in the pass from Dalton, and the Texans celebrated moving to 4-5 when the review eventually confirmed the decision.