Shayne Graham kicked four field goals for the Texans, while Foster finished with 140 yards and became the first NFL player to have 100-yard games in each of his first three playoff games. Watt finished with a sack and swatted away two of Andy Dalton's pass attempts, once wagging his finger at the Bengals quarterback after the play.
The Texans had trouble finishing drives and managed three field goals in the first half against the Bengals (10-7). Houston struck first after the break, with Foster scoring the game's only offensive touchdown to make it 16-7.
Schaub, who missed last year's playoffs with a foot injury, had an interception returned for a touchdown by Leon Hall before halftime.
"It was never easy," Schaub said. "Cincinnati is a great team. I made a turnover and gave them points. We just had to rally around each other and we did that."
"I think it was a full defensive effort, everybody was flying around and we were getting off the field on third downs," Watt said.
The Texans rebounded from a terrible month where they lost three of four games and the No. 1 seed in the AFC playoffs. The win came in front of a record crowd of 71,738, including former Oilers great Earl Campbell.
"We like to run the ball and play good defense," Foster said. "It only takes one week to turn things around in the NFL and we did that."
Schaub shook off his first-half miscue to finish 29 of 38 for 262 yards.
The Bengals couldn't do anything offensively before the break, and were outgained 250-53 in the first half. Dalton was 4 of 10 for 3 yards in the first half. He finished 14 of 30 for 127 yards.
Houston piled up 351 yards and held the ball for 32 minutes through three quarters, but got into the end zone only once.
Dalton's 45-yard pass to A.J. Green got Cincinnati moving in the third quarter and set up Josh Brown's 34-yard field goal. When Dalton tried to go to Green again, Joseph intercepted and got the Texans in scoring range again as the quarter ended.
The main difference in this one: Schaub was back in charge for Houston. Rookie T.J. Yates filled in for Schaub, got the Texans a win in their first-ever playoff game, but couldn't take them any farther.
It became a pattern -- move the ball down the field, settle for three points. The fans started booing.
And then Schaub did the one thing he wanted to avoid -- he let Cincinnati's defense get its hands on the ball. Hall anticipated Schaub's throw, stepped in front and returned it untouched, high-stepping the last few yards, for the defense's fourth touchdown in the last four games.
Hall also ran back an interception 17 yards for the only Bengals touchdown in a 13-10 win over Pittsburgh that clinched a playoff spot. It was the first interception return for a touchdown against the Texans this season.
Like the Texans, the Bengals ended the season by hitting a wall on offense -- one touchdown in the last two games. The offensive woes continued on Saturday when the Bengals failed to score a touchdown on offense again.
Copyright 2013 by The Associated Press