Now the Texans (8-1) are preparing for one of the NFL's worst teams in Jacksonville, focused on improving as they inch closer to their goal of reaching the Super Bowl.
Houston coach Gary Kubiak believes Sunday's win will help his team in the future.
"The more ways you find to win in this league, you get more confidence," he said. "Things like that give you a chance to be a great team. There will be nothing false about what we are when we get there at the end because we've been in some tough situations. And the more we handle them, the better we get."
He said winning a tough game on the road was particularly important with games at New England and Indianapolis coming up in the second half of the season.
Kubiak sees the Texans maturing, and knows that will be key if they hope to become a championship team. He talks to his team often about getting to that goal.
"Can you be a good enough football team or a good enough organization to win a championship," he said he asks his team. "I think there are different levels and we're trying to work our way toward that mindset."
The Texans got the 13-6 victory on Sunday by forcing four turnovers and grinding out the win with their running game led by Arian Foster's 102 yards rushing and the game's only touchdown on a 2-yard reception.
Foster is third in the NFL with 872 yards rushing. Kubiak has been pleased with him all season, but thought his work on Sunday night was particularly impressive.
"I would say that was about the toughest 102 yards a man could get," Kubiak said. "If you look at some of the great games he's had, I don't think there's anything bigger than last night because we were running against eight-, nine- man fronts all night. Everybody and their brother knew who was getting the ball and he still found a way to keep us on track."
Houston's line led by end J.J. Watt, usually leads the way defensively. But against the Bears, it was the secondary that came up big. Safety Danieal Manning, a former Bear, led the way with an interception and a forced fumble.
But that wasn't the only way he contributed to the win.
"He did a really good job with our team the night before the game, just talking about what it was going to take to win in that place," Kubiak said. "He's a leader on this team and a fine player. I thought he did an exceptional job with the rest of his teammates this week letting them know what it was going to be like, how we were going to have to play to win that game."
Cornerback Kareem Jackson also had an interception for the Texans. Jackson has shaken off a slow start to his career to emerge as a solid member of Houston's defense in his third season.
"We all know what Kareem's been through," Kubiak said. "Good pros, they go through tough times early in their career, but then when they come out of it, they're consistent and good for a long, long time. I think that's what you're seeing from Kareem."
The Texans could get a boost this week with the return of a trio of injured players. Running back Ben Tate, who has missed the last two games with a hamstring injury, has been running with trainers and could play on Sunday.
Nose tackle Shaun Cody (ribs) and tight end Owen Daniels (back), who sat out Sunday, are also better and should return to practice this week. Cody will go through what Kubiak called a trial run on Wednesday.
"If he's able to work through that situation I think you could see him on the field probably Thursday or Friday," Kubiak said of Cody. "We're heading toward him being back active and being a part of it."