The Tulane baseball team found its Sunday starter against Houston on a chilly, windy day at Turchin Stadium.

But the Green Wave came oh-so-close to achieving much more before a heated conclusion to a crazy series that featured a rare ejection of coach Travis Jewett and some customary wildness out of the bullpen.

With a chance to sweep the Cougars in what would have been a transformative weekend, the Wave lost 5-3 in the second half of a doubleheader caused by a rainy Saturday when it could not hold on to a 2-0 lead freshman pitcher Josh Bates handed it.

Three relievers combined to walk four batters and hit another as Houston scored five times in the final three innings, including a pair of four-pitch free passes by Will McAffer (0-3) in the ninth.

Jewett was especially frustrated with the walks.

“I’d be a lottery winner if I had that answer right now,” he said. “The park just played to contact today with the way the flags were blowing. You could almost just throw it in there and let them hit it. You can’t defend the walk.”

A win would have pulled Tulane into a first-place tie in the American Athletic Conference less than 48 hours after it was next-to-last in the league standings and trending down, trailing Houston 13-3 in the sixth inning of Friday night’s opener before rallying for a jaw-dropping 17-16 victory.

Instead, Tulane (16-21, 6-6 AAC) fell into a tie for sixth in the tightly bunched race, one game behind co-leaders Houston (21-14, 7-5), South Florida and Cincinnati. The Wave, which beat the Cougars 2-0 in the opener of the doubleheader earlier Sunday, missed several opportunities to finish them off.

Bates struck out nine through six innings in his first weekend start, allowing zero runs to that point.

“I was getting a lot of first-pitch strikes and found a groove,” he said. “I felt pretty confident out there.”

Tulane imploded when he left with runners on first and second and one out in the seventh.

After Houston went ahead 3-2 with three quick runs, the Wave’s Kody Hoese tied it with a two-out RBI single in the bottom half, but third-base umpire Matthew Hensel called catcher Acy Owen out as he slid into third base.

Owen leaped up to argue, and Jewett was tossed for the first time this season when he came out to defend him.

“I saw the throw was going to be on the left side of the bag, so I tried to slide to the other side and get my hand in,” Owen said. “I thought I did.”

Said Jewett: “I saw safe. I thought it was a missed call.”

Hensel departed soon after Jewett, leaving to catch a plane as the game finished with only two umpires.

Tulane missed another opportunity when Houston closer Carter Henry (4-1), who surrendered five runs in the ninth on Friday, struck out Tyler Heinrichs with the bases loaded to end the eighth.

The Cougars scored the winning run when a blooper landed just past the outstretched glove of shortstop Sal Gozzo with the bases loaded again. Gozzo then held on to the ball after picking it up, allowing an insurance run to cross the plate.

Keagan Gillies (3-4), who lost two 1-0 games earlier this year, was on the right end of a low-scoring affair earlier Sunday, outdueling Houston’s white-hot Aaron Fletcher. Gillies limited the Cougars to two hits through five innings, stranding runners in scoring position in each of the last four.

The Wave scored two runs off of Fletcher (4-2), who entered with an AAC-best ERA of 1.03 before allowing a season-high eight hits. Jonathon Artigues’ two-out, two-strike single in the third drove in Owen for the only run Tulane would need.

Ben White pitched the final two innings of the seven-inning game for the save, capping off an incredible week. He picked up his first victories of the year in his previous two appearances as Tulane won in walk-off fashion against UNO and Houston.

White was not available later in the day, and Tulane missed a chance to sweep Houston for the first time since 2003.

“Any game you lose isn’t good, but it was a great series win for us,” Artigues said. “We played hard all weekend."

Follow Guerry Smith on Twitter, @guersmith