HOUSTON -- Slowly but surely, Andy Dalton and the Cincinnati Bengals are exorcising the last few demons that have haunted them the past three seasons.

First, it was winning a game at Baltimore. The Bengals hadn't done that since Dalton became their starting quarterback in 2011.

Then, it was winning a game in Houston.

Check and check.

Twelve weeks after easing past the Ravens with a season-opening win on the road, the Bengals tip-toed by the Texans on Sunday afternoon at NRG Stadium, finally scratching off one of the most toughest items left on their to-do list. After two straight postseason trips (2011 and 2012) ended with opening-round losses in Houston, Sunday's win was all the more sweet for the Bengals. That is because this game marked the first time since those postseason losses that they were back in Houston.

"This was another one of the monsters we hadn't beaten yet," veteran offensive tackle Andrew Whitworth said. "To be able to come do it against a team that really found themselves last week in Cleveland, and to win on the road in a tough place against a tough defense that had played well and thought they had all the confidence in the world, there was a lot to play here.

"We had to come in here and prove we wanted it."

Dalton might have had the most to prove, considering his hometown of Katy, Texas, is about a half hour west of NRG Stadium. He also hadn't performed well in his two previous trips to the stadium, throwing four interceptions and zero touchdowns in the two losses.

After the game, Dalton was so relieved by finally getting a victory near his hometown that he autographed his grass-stained, game-worn jersey and gave it to his dad Greg as part of his 55th birthday present.

"The last couple of times we have come here, the last couple of times I have been in this room right here, it hasn't gone in our favor," Dalton said after the game. "We don't have to worry about anybody talking about that anymore."

Just like no one has to talk about how Dalton was 0-for-3 in his career playing at Baltimore before this year's 23-16 win there.

What other demons are out there waiting to be exorcised by Dalton and the Bengals? The postseason-win demon.

If the Bengals keep winning, they will have a chance in few weeks to finally win their first playoff game in 24 seasons.