But the Cougars went down swinging.
A basket by Damyean Dotson with 35 seconds left gave Oregon a 96-94 lead in overtime Oregon's first lead since it was 2-0 seconds into the game, and the Ducks held on.
With the game tied at 94-94, the Cougars thought they had taken the lead when Frank Bartley scored on a driving layup. But Bartley was hit with an offensive foul, and the basket wiped away.
Oregon's Elgin Cook could have won it with 1.8 seconds remaining in regulation, but missed a pair of free throws, and the game went to overtime. Oregon improved to 11-0. BYU enters WCC play next week with an 8-5 record.
The Cougars led 83-76 with 3:52 remaining in regulation after a pair of free throws by Matt Carlino, but couldn't hold the advantage.
They scored just one point a free throw by Nate Austin, shortly before he fouled out during a seven-possession stretch, and the Ducks came from behind to force overtime.
The Cougars played in overtime without big man Eric Mika, who fouled out at the end of regulation, sending Cook to the line.
Basically, the Cougars lost the game at the free-throw line, going 23 of 34 from the charity stripe.
After playing incredibly well in the first half - the opposite of last week's start against Utah - the Cougars stretched a six-point lead to 10 with 15:27 remaining when Kyle Collinsworth hit a free throw.
But OU's Johnathan Loyd, scoreless in the first half, seemed to get the Ducks going with a pair of free throws, and a big 3-pointer by Jason Calliste got the home team to within three with 12:40 left.
Each time the Cougars threatened to pull away in the middle of the second half, the Ducks would reel them back in. But each time Oregon's crowd got into it after a basket, the Cougars would answer.
It made for a thrilling finish.
The Cougars played one of their better first halves in the Dave Rose era, at least in a true road game.
Haws got off to one of his trademark fast starts, making his first four shots for nine points before the first media timeout. He scored 18 points in the first half on 7 of 9 shooting. The Cougars had a 14-11 lead at that point, and kept their foot on the gas the rest of the first half.
BYU shot 56.7 percent from the field in the first half, including 50 percent (4 of 8) from 3-point range.
The Ducks were content to fire from the perimeter, and shot just 40 percent in the first 20 minutes. They were out rebounded 25-14 in the first 20 minutes, despite coach Dana Altman sending wave after wave of big players into the game.
After point guard Matt Carlino failed to register an assist in last week's 81-64 loss at Utah, BYU coach Dave Rose made a minor adjustment to his offense, having Kyle Collinsworth bring the ball up court in the point-guard role and Carlino playing on the wing. The Cougars led by as many as eight points in the first half, on a couple of occasions, but could never pull away. They missed five free throws before the break, and committed 10 turnovers by playing their uptempo style.