The Texans reversed a late-season slide of three losses from their last four games by stopping the Bengals attack cold, while Houston's blend of the run and pass dominated a game that had six field goals, four by Houston.
Arian Foster rushed for 140 yards and a touchdown on Saturday as the Texans ousted the Bengals in the first round for the second season running.
"The whole stadium knew we had to line up and run the ball and boy, he was at his best there at the end," Gary Kubiak, the Texans coach, said afterwards.
"He's become a fine, fine player, and it just seems like the bigger it gets, the better Arian gets."
The result books Houston a second-round meeting with American Conference contenders the New England Patriots next weekend.
Foster added eight catches for 34 yards and became the first player in NFL history to rush for at least 100 yards in the first three postseason games of his career.
Texans quarterback Matt Schaub, who missed last season's 31-10 playoff win over Cincinnati with a foot injury, completed 29-of-38 passes for 261 yards with one interception in the first postseason start of his career.
Houston's defence played a key role, holding Bengals quarterback Andy Dalton to just 127 passing yards with one interception.
The first day of playoff action included the Minnesota Vikings at the Green Bay Packers in a National Conference contest.
The Vikings announced before the game that quarterback Christian Ponder would be inactive because of an elbow injury.
Ponder was hurt last Sunday in the Vikings' 37-34 win over the Packers in the teams' regular-season finale.
Ponder tested his arm in pregame warm-ups, but was declared inactive shortly thereafter.
Backup Joe Webb, who didn't attempt a pass all season for the Vikings, got the start in place of Ponder.
"The offence didn't play as well as it could have," Dalton said following the game. "You can always look back and say, 'What if?"'