For a team that had won two of its past 12 games, Tulane was talking big before it traveled to Hartford, Connecticut, for the American Athletic Conference men’s basketball tournament.

The self-belief stemmed from the Green Wave’s success on the road. Tulane (15-15, 6-12 AAC) improved to 5-4 in conference road games by beating South Florida 67-63 on Saturday — its first winning mark away from New Orleans in 18 years — and planned to take that prowess to the XL Center for its first-round matchup with No. 10 seed Houston (12-18, 4-14) on Thursday.

“This team has the confidence they can line up and play against anybody,” coach Ed Conroy said. “To go on the road and win, you have to have a certain character and toughness and resiliency about you.”

Conroy saw a lot to like against South Florida, which was coming off a 31-point victory against Central Florida. The Wave shot 48.1 percent — its best mark since the league opener at East Carolina — while outrebounding the Bulls 32-22 and committing a season-low six turnovers.

Individually, the signs were just as good.

Guard Jonathan Stark scored nine points in the final five minutes while hitting all four of his shots during that span. He had scored eight or fewer in his past four games and shot 28 percent in 15 games after being named AAC Player of the Week in early January.

“I was real happy to see him try to take over and show his old form,” teammate Louis Dabney said. “He was getting back in the mode of being comfortable that he could take his guy.”

Reserve forward Payton Henson scored 13 points on 5-of-6 shooting, reaching double figures in consecutive games for the first time. After hitting six of his first 50 3-point attempts, he has gone 3-for-3 from long range in the past three games, giving the Wave some punch off the bench.

“We are a completely better team when Payton is playing that way,” Dabney said. “I know the numbers say he probably can’t shoot, but it’s all a mind thing with him. When he’s into the game and he’s focused, he can be a great shooter from deep.”

Guard Jay Hook was 6-of-8 from the floor for 16 points, his best output in three weeks.

“It was good that we got that win before the conference tournament,” Hook said. “We executed some stuff that we worked on in practice. If we do our keys at a high level, we’ll win four in a row (for the tournament title).”

First, they have to get by Houston, which has won three straight under new coach Kelvin Sampson after starting 1-14 in the AAC. The Cougars sandwiched an overtime victory on Tulane’s senior night with a 17-point win against South Florida and an 18-point shellacking of East Carolina.

Houston guard Jherrod Stiggers scored 17 in each of his past two games.

“We’re a long way from a great team, but if you have a good program, you see improvement as the year goes along,” Sampson said. “We’ve gotten better and better, and that’s what excites me about where we are now.”

Tulane led Houston for the first 16 minutes of the second half before losing in overtime last week.

“We felt like we let one fall and they stole one from us,” Dabney said. “When we play again, it’s going to be a totally different game. They’ll get our best game.

If Tulane survives Houston, recent and long-term history says the run will end there. The winner plays Friday against No. 2 seed Tulsa (21-9, 14-4), which walloped the Wave 76-55 in Tulsa last month to complete a season sweep.

Tulane has not won two games in the same conference tournament since 1983, when it was in the Metro. Then again, it’s been a long time since the Wave has felt this good about its performance in unfriendly environments.

“It’s good going into the tournament with a win under your belt and feeling like you’re in rhythm again,” Henson said. “We have to continue to bring that concentration on the road and compete.”