"It feels extra sweet because they were undefeated," Utah guard Danielle Rodriguez said.
It was extra disappointing for the Cougars, who had a five-point lead, 62-57, with three minutes remaining in regulation but failed to score after a pair of Lexi Eaton free throws.
Plouffe, who finished with a game-high 24 points, made a jumper from just inside the arc with a minute left in regulation, and when Eaton missed a heavily defended layup with 35 seconds left, neither team got off a decent shot after that.
"It is all about who had ice in their veins at the end, and she had it," Rodriguez said.
Bailey Morgan's 3-pointer with 10 seconds left in the first overtime gave BYU a 67-65 lead, but after a timeout the Cougars let Plouffe drive down the middle of the paint for an easy layup.
"I've lost two games to them in five years, and she has done it both times," said BYU coach Jeff Judkins. "… She just seems to step it up against us more than the other games."
Judkins said he told the Cougars not to let Plouffe touch the ball out of the timeout with 6.8 seconds left, but they did, then were too worried about giving up a 3-pointer and the All-American beat them off the dribble.
In the second overtime, Plouffe hit a 3-pointer on Utah's first possession, and the Cougars missed their first six shots, looking tired.
"It just looked like we were fresher," said Utah coach Anthony Levrets.
Emily Potter added 18 points for Utah before fouling out and Rodriguez added 15.
Eaton led BYU with 20 points, but the Cougars' other star, Jennifer Hamson, had just nine and was a non-factor in the first half, going scoreless and without a blocked shot or a rebound.
Hamson picked up two fouls before three minutes were off the clock, and spent much of the first half on the bench.
"That killed us," Judkins said.
With Potter carrying the scoring slack in the first half for Plouffe, who also had two fouls early in the game, Utah moved out to a 23-13 lead. Potter led all scorers in the first half with 14 points.
The Cougars got back into the game with an 8-0 run, and tied it 27-27 with 3:54 remaining on Eaton's 3-point play.
BYU led 34-33 at halftime, thanks to five quick points by Eaton in the last two minutes.
"I'm just thrilled to get out of here with a win," Levrets said.
Storylines Utes persevere in Provo for win
R Utah's Michelle Plouffe makes last-second baskets to force the first and second overtimes, and the Utes roll in the second overtime to end BYU's nine-game winning streak to start the season.
• It was the first time a BYU-Utah women's game has gone to overtime since 1995.