Tulane is 2-0 in a conference tournament for the first time since 2005, and with the way things have turned totally upside down in Clearwater, Florida, is in prime position to go farther.

Seeded seventh in the eight-team American Athletic Conference field after setting a school record for losses, the Green Wave run-ruled No. 6 seed Memphis 12-2 in eight innings on Thursday, joining No. 8 seed South Florida as the only undefeated teams remaining.

To reach Sunday’s championship game and a chance to earn an automatic bid to an NCAA regional, all the Wave (17-39) needs to do is not lose twice in row on Saturday to the winner of an elimination game between No. 2 seed Houston (34-22) and Memphis (29-27) — the two teams it already has beaten.

“That’s the mission, right? To get into that position where you’re controlling your destiny with a healthy, full-rested bullpen and a day off to boot to get yourself in a good space,” Tulane coach Jay Uhlman said. “Our guys had intent, they were purposeful and they came to play good baseball tonight.”

This one was all about an outstanding bounce-back performance from pitcher Dylan Carmouche (3-8) and clutch production up and down the lineup. Carmouche, who had allowed 15 runs in five innings over his last two starts, limited the Tigers to three hits and struck out nine while going the distance. He permitted only three base runners after two walks led to a pair of runs in the second inning.

He set the tone by throwing his first seven pitches for strikes.

“All I’ve been working on is just attacking early and getting my fastball for strikes,” he said. “That’s really what I tried to do today, and it worked out.”

Carmouche was on the opposite end of a 12-2 run-rule loss at Memphis six days earlier, but he began and ended the rematch with strikeouts, outdueling AAC pitcher of the year Dalton Fowler (5-6).

“He changed speeds, pitched on both sides of the plate and kept us off balance,” Memphis coach Kerrick Jackson said. “Tip your hat off to him. That’s the best I’ve seen him pitch this year.”

Fowler, who had a 2.21 ERA against Tulane in four outings, could not match Carmouche, leaving in the seventh inning with a 6-2 deficit. Tulane then clobbered relievers Carson Stinnett and Jackson Lyons.

Designated hitter Brennan Lambert drove in at least one run in all four of his plate appearances, finishing with a career-high five RBIs. The last two came when he took a pitch off the plate the opposite way to the wall for a two-run double — his second of the game after hitting one off Fowler that lodged between two walls in right field for a ground-rule double.

“That was our biggest game of the year, and I think we prepared for it,” Lambert said. “He’s a great pitcher, so we knew it was going to be a tough day, but we enjoy that and embrace it. Our intensity, our want and our will was there. We had a good plan and stuck to it all day with good at-bats.”

Tulane benefited from three defensive mistakes while scoring three runs in the sixth to a break a tie at 2 — a throw in the dugout at the back end of a double-play attempt, a misplayed fly ball that turned a routine out into a double and Fowler slipping on the wet ground as he tried to field a squeeze bunt from Lambert. But the Wave dominated this one in all aspects.

Third baseman Simon Baumgardt made a terrific stab and throw for the final out of the first inning, setting the tone. Left fielder Brady Hebert and right fielder Jake LaPrairie made back-to-back running catches at the wall after the Wave went ahead 5-2 in the sixth.

Memphis killer Teo Banks provided the final blow, launching his fifth home run in as many games against the Tigers in the eighth to account for the final margin.

When Carmouche retired three in a row, the game was over early.