Haws, who had a tough time shooting the ball from the field on the night (5-of-19), was 14-of-14 at the free-throw line for the second-seeded Cougars (23-10) as they advanced to the conference title game.
This is the first time in the league. Haws ended up leading all scorers with 24 points, followed by Kyle Collinsworth with 18 points and a game-high 12 rebounds.
Also with a double-double for BYU was Eric Mika with 11 points and 10 boards, while Anson Winder and Matt Carlino pitched in with 15 and 11 points, respectively.
The third-seeded Dons (21-11) were led by Cole Dickerson with 20 points and 10 rebounds, followed by Matt Glover with 14 points before he picked up his fifth personal foul.
Off the bench, Tim Derksen accounted for 11 points, while Avry Holmes responded with 10 points, seven assists and four steals in the setback.
The Cougars opened the contest on a 12-4 run and led by double digits less than seven minutes in, but even after shooting 50.0 percent from the field through the first 20 minutes, BYU actually trailed by two at the break, 37-35.
Late in the second half the Dons put together an 8-0 run to knot the score at 64-64. Both teams went cold down the stretch, with the Cougars working to take what should have been the last shot in the waning moments, but they had their attempt blocked, resulting in the game going to overtime.
BYU was held scoreless for more than six minutes at the end of regulation.
The Dons fell behind right away in the bonus session and didn't convert a field goal attempt until the period was half over. On the other side, Haws had six of the first eight points for the Cougars and then stepped to the charity stripe late to secure the win.
In addition to owning a 45-35 advantage on the glass, the Cougars also outscored USF at the free-throw line by a 24-12 margin.
With the victory, BYU advances to the title game against Gonzaga which defeated Saint Mary's earlier this evening in the other semifinal matchup, 70-54.