Tulane’s spot atop the American Athletic Conference turned out to be fleeting.

After pulling into a five-way tie for first place Friday night, the Green Wave fell victim to a season-long issue for the rest of the weekend: its inability to do much of anything against good pitching.

In this case, make that really good pitching.

Shut out Saturday on a four-hitter by Houston right-hander Kyle Dowdy (7-1, 2.77 ERA), Tulane managed five hits against freshman left-hander Seth Romero (6-3, 1.80) on Sunday and failed to score until the ninth inning, losing 7-1 at Turchin Stadium while at least avoiding its seventh shutout.

The back-to-back power outages dropped the Wave (29-18, 9-9) to .500 in the conference and into fifth place, two games behind co-leaders Houston (32-16, 11-7) and East Carolina and a game behind South Florida and Memphis with two regular-season series left.

“You can talk SEC, ACC; you can talk any league in the country,” Tulane coach David Pierce said. “When those two guys (Dowdy and Romero) are right, they are as tough as anybody.”

Tulane finally ended an 18-inning scoreless drought on Lex Kaplan’s double in the ninth after Tyler Wilson had doubled earlier in the inning.

“It’s very frustrating because we need to win games,” Kaplan said. “We want to play in the postseason, and we want to make a regional, and it would be nice to get an at-large bid. We need to come out next week and do better than we did this weekend. It just all around wasn’t a good team effort.”

The closest the Wave came to scoring early was in the third, when catcher Jake Rogers flew out to deep center, just in front of the warning track, for the last out with runners at the corners. By that time, Tulane already trailed 5-0.

Junior-college transfer Patrick Duester (5-5), making his first weekend start of the season, left in the third inning despite cruising through the first inning on only four pitches. Houston touched him for two runs in the second on a pair of singles and a double, then chased him in the third after two walks and two singles led to three more runs.

“I felt good the first inning, and after that until I came out I threw maybe three pitches that I was satisfied with,” Duester said. “I can’t really explain what happened, but I just never established any of my pitches. My breaking ball was just spinning out of my hand.”

The Cougars added another run in the fifth with three consecutive singles off reliever Emerson Gibbs, who lost his spot in the weekend rotation after a shaky outing at Cincinnati last Saturday. Gibbs did not make a strong case that he should have kept his role, giving up four hits and walking two in two innings.

Eight Tulane pitchers allowed 13 hits and walked eight.

The only saving grace for Tulane was its fielding. The Wave, which had its first errorless weekend, turned a sweet double play in the seventh when second baseman Jake Willsey slid to his right to stop a ground ball and flipped to shortstop Stephen Alemais, who made a quick relay to first.

It didn’t help. In the bottom of the inning, Romero retired the Wave on three straight fly balls. Romero (6-3), who began the year as closer and has five saves, came within two outs of his first complete game.

“I just think it’s much more mental than anything,” Pierce said. “And then you get frustrated when you’re facing good stuff like today.”

Tulane will get another crack at a team in front of it in the AAC standings next weekend when South Florida visits Turchin Stadium. Before then, the Wave has a minibreak with no midweek game and no practice Monday and Tuesday as it enters final exam week.

“Right now, I think we are in a little bit of a zombie mentality,” Pierce said. “I think exams kick in more than people acknowledge when you’re playing a good team like (Houston). We’ll let their bodies and mental side of the game just kind of get away for a couple days and rest.”