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BYU's Lexi Eaton (21) walks off the court after BYU's 70-51 loss to Connecticut in a regional semifinal in the NCAA women's college basketball tournament in Lincoln, Neb., Saturday, March 29, 2014.

LINCOLN, Neb. — Clinging tenaciously to a six-point lead with less than five minutes remaining in the first half against No. 1 UConn, BYU seemed to be on the verge of making history, poised to shock the women’s college basketball world.

The undefeated Huskies, who had trailed for only 39 minutes — out of 1,440 minutes — all season long going into Saturday’s Sweet 16 matchup, seemed rattled.

“We knew it was possible,” said forward Morgan Bailey, “to beat the No. 1 team.”

UConn’s perfect season, and 42-game winning streak, appeared to be in some jeopardy.

But that vibe before a crowd of 9,585 at Pinnacle Bank Arena — that the Cougars could stage one of the biggest upsets ever in the NCAA tournament — was relatively short-lived.

Eventually, the Huskies did what they usually do. They made a run at the end of the first half to take a one-point halftime lead, then pulled away midway through the second half to claim a 70-51 victory over No. 12 seed BYU (28-6) and improve to 36-0.

“We knew that if things kept going the way we wanted to and if we kept executing our plays, that it was going to be a close game right down to the wire,” said guard Kim Beeston, who led the Cougars with 16 points and four 3-pointers. “I think that’s why we were a little disappointed that we weren’t able to do that. But I think we really showed what we can play like in the first half. It’s just too bad that we couldn’t play that way the entire game.”

“We played some of our best basketball,” said coach Jeff Judkins. “I think we just got a little tired in the second half. We weren’t quite as sharp. But I’m really proud of these ladies.”

And with that, the Cougars’ Cinderella run in the NCAA tournament came to an end. They were only the third No. 12 seed to advance to the Sweet 16 in tournament history.

Though they lost, let’s put the magnitude of what they accomplished in perspective.

BYU actually led for nearly 10 minutes against UConn. A basket by Lexi Eaton to start the second half, with 19:40 remaining in the game that made the score 31-30, marked the Huskies’ first second-half deficit of the entire season.

“They’re definitely beatable,” said Bailey, who had 14 points. “If we had come out the way we did in the first half, we could have gotten them. We kind of sat back on our heels and never regained balance. They’re definitely beatable.”

UConn coach Geno Auriemma said he wasn’t surprised to be tested so vigorously by BYU.

“I knew it was going to be like this because they are not an easy matchup for anybody,” he said. “The way they played in the first half and the way we shot in the first half, that is the kind of stuff you have to expect in the tournament.”

Huskies forward Kaleena Mosqueda-Lewis poured in a game-high 19 points and pulled down 13 rebounds. UConn outscored the Cougars in the paint, 36-12, and scored 27 second-half points.

“I thought we showed a lot of who we are that second half,” Auriemma said. “I thought we picked up the pressure in the second half. We made them play much faster. I thought Jeff did a great job controlling the tempo in the first half. They did a lot of crazy stuff. They were changing things up all the time, because they were scoring.”

UConn and BYU were tied, 37-37, after a putback by Bailey with less than 17 minutes remaining. But that was as close as the Cougars got the rest of the way.

A 10-0 run put the Huskies up by double digits for the first time. A 3-pointer by Kim Beeston cut the deficit back down to six, but then UConn enjoyed a 16-2 spurt to seize a 68-48 advantage with 4:30 left.

BYU stayed close in the opening minutes of the game, and grabbed a 17-15 lead midway through the first half. The Cougars extended their lead to 27-21 thanks to a scoring flurry by Beeston. She scored 14 of her 16 points during a six-minute stretch in the first half, including three 3-pointers.

“We came out confident, like we did in the first two games of the tournament,” Bailey said. “They weren’t pressuring us as hard, and we executed really well and played together as a team really well.”

In the first half, BYU knocked down 5 of 10 3-pointers while UConn was 0 of 8 from 3-point range. Beeston hit three 3s and Bailey drilled two.

UConn’s Bria Hartley was held scoreless in the first half, and Breanna Stewart had just four at intermission. But Stewart finished with 16 points, and Hartley had 12.

“The key to slowing down Connecticut is to make baskets,” Judkins said, “and not letting them fast break. You noticed every time we missed or every time there was a turnover, it was like three-on-two running back to match up with them. I saw the stat on TV that they are the highest-scoring fast break team in the country. Well, they are. They run like deer and they jump out of the gym.”

“In the second half, we let a few possessions get away from us, and that’s when they went on their run,” said Eaton.

BYU held UConn to 39.4 percent shooting, the second-lowest of the season for UConn. The Cougars also limited the Huskies to season lows in 3-point percentage (15.8) and 3-pointers (three).

BYU ended its season with a program-best 28 victories.