Now comes the big test. The Texans (13-4) move on to the second round on Jan. 13, when they visit the New England Patriots, who beat them 42-14 in Week 14. This time they're 9½-point underdogs.
"It's one step," Watt said of the win. "We know what it means, and we have bigger goals than that."
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.
"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 defense smothered Dalton and the Bengals early. Their second drive ended when Connor Barwin tackled BenJarvus Green-Ellis for a 6-yard loss and Watt followed with a sack of Dalton.
Houston's offense had the ball for almost 39 minutes as it ate up the clock with a season-high 32 carries from Foster.
"We controlled the line of scrimmage, and any time we do that it's going to be hard to beat us," Foster said.
Johnathan Joseph, a former Bengal, came up with an interception for the Texans, who kept Cincinnati without a playoff win since the 1990 season, the league's longest current streak.
The Bengals had a chance for a touchdown late in the fourth quarter, but Dalton's pass sailed just out of reach of a diving A.J. Green in the end zone.
"The offense didn't play as well as it could have," Dalton said. "You can always look back and say, 'What if?' "
O Arian Foster rushes 32 times for 140 yards as the Texans hold the ball for almost 39 minutes.
• Bengals QB Andy Dalton, flustered by the Texans' defense, is just 14 for 30 for 127 yards and an interception.