Haws, the WCC player of the year, had a hard time freeing himself from San Francisco's defense, shooting 5 of 19, but made all 14 of his free throws
His teammates helped pick up the slack, sending the Cougars into Tuesday's championship game against Gonzaga.
Kyle Collinsworth had 18 points and 12 rebounds, and Anson Winder had 14 points for BYU (23-10).
San Francisco (21-11) fought back several times, including a late run in overtime. Matt Glover hit a 3-pointer with 28 seconds left and the Dons had a shot to tie after Winder made 1 of 2 free throws, but Avry Holmes missed a fadeaway jumper just before the buzzer.
Cole Dickerson led the Dons with 20 points and Glover had 14.
BYU made a strong case for an NCAA tournament bid at the close of the regular season, winning seven of its final eight games. The Cougars beat Loyola Marymount to open the WCC tournament, but were still teetering on the NCAA bubble and couldn't afford a loss to San Francisco.
The Dons lost both games to BYU during the regular season, but played well down the stretch as well, winning 10 of their final 12 games, including six straight.
It looked like it was going to be easy for the Cougars early.
BYU hit six of its first eight shots and kept firing, building the lead to 27-17 on a 3-pointer by Anson Winder from the corner.
But San Francisco fought right back, going a 10-2 run, then fighting the Cougars for every inch, particularly Haws.
The Dons made life difficult on the conference player of the year, knocking him around when he went to the basket, challenging when he shot from the perimeter. Tim Derksen swatted one of his 3-point attempts in the first half, drawing a loud cheer from the small-but-vocal contingent of San Francisco fans, and Haws had to get six of his 10 first-half points from the free-throw line.
San Francisco led by two at halftime and the second half was like a heavyweight fight, the teams traded blows and baskets, neither able to gain much of an advantage.
Haws continued to labor in the second half, missing a couple of open shots before scoring on a putback off his own miss. He became frustrated late in the second half, grabbing Glover's arm after the San Francisco guard took the ball from him.
Haws wasn't part of the action for a long stretch of the second half—on the bench and even when he was in—and that's when Matt Carlino took over for a stretch. He scored on a three-point play, slapping hands with fans on the front row after the ball went through, then added a 3-pointer from the corner and another three-point play on a drive, putting the Cougars up 58-51.
The Dons wouldn't go away, clawing back to tie it at 64-all on Mark Tollefsen's 3-pointer in the corner with just over 3 minutes left.
BYU had a shot to go ahead after getting the ball with 33 seconds left in regulation, but fumbled it away, waiting too long to get a shot off before settling for a 3-pointer by Collinsworth that was blocked by Derksen.