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Now they're back to Conference USA play, looking for their first league win against Tulane after shaking off that embarrassing conference-opening loss at UTEP.
The Cougars may have moved on from that defeat, but they certainly haven't forgotten it. The 58-41 upset by the Miners dropped No. 12 Houston out of the poll altogether.
"I heard someone say that we're tied for first in the SEC and Big 12 South, but tied for last place in C-USA," quarterback Case Keenum said. "None of that matters, what we've done in non-conference. Those wins were good, but that shows how much they mean."
Coach Kevin Sumlin is happy with the mindset of his players and knows they're not content with what they've accomplished so far.
"I like our edge," he said. "Just talking to the guys, our team feels that we still have a lot to prove. As long as we continue with that attitude, our preparation will continue to be good."
Houston is the first C-USA team to beat three BCS conference teams since Louisville did it in 2003 and the first non-BCS team to do it this season. The Cougars know getting back on track in league play is key to their goal of winning the West division of C-USA.
"This is the biggest game of the season right now," receiver Tyron Carrier said. "We didn't have a very good performance against our last C-USA opponent so ... it has to be the biggest. We're last in our league right now and haven't won a game. Our last performance wasn't up to par. We need this win."
Houston has the nation's most potent offense and is gaining more than 569 yards a game. Much of that success has to do with the play of Keenum, who is No. 1 in total offense (438.8) and passing yards per game (426).
Keenum has thrown for at least 350 yards in each game this season and had 434 yards passing and four touchdowns in Saturday's 31-24 win over Mississippi State. The unassuming junior credited his receivers for his success.
"I was watching a rerun of the game and I saw how many yards after catch we have, and it's just amazing how those guys get up the field after they catch it," he said. "It says a lot about the talent of our guys and the schemes the coaches give us. That's the plan, to get the ball in the hands of those guys, and they can do special things with it."
Keenum and the Cougars will have a challenge this week against a Tulane pass defense that is allowing a conference-low 197.2 yards a game.
"I just have to make sure I'm the most prepared football player out there on the field," Keenum said. "I need to be able to get in a good play, make a good read, and then throw a perfect pass."
Houston's defense remains among the worst in the nation, allowing more than 450 yards a game. The Cougars gave up more than 300 yards rushing for the second straight week against Mississippi State but forced four turnovers after coming up empty against UTEP.
Linebacker C.J. Cavness said forcing more turnovers is a focus for the group.
"With our high-rated offense, the more we give them the football, the more opportunities they get to score," he said. "As a defense, that's our job to get stops and give the ball back to the offense. We have to be opportunistic."
