Olson, a 23-year-old redshirt sophomore, sprained his left knee with 6:47 to play in the first quarter when he took a hit after an incomplete pass and did not return.
Cowan took over for UCLA (4-1, 2-1 Pac-10) and completed the first four passes of his college career, including a 10-yard TD toss to Marcus Everett for the first points of the game.
Cowan also threw a 15-yarder to Matt Willis in the second.
The Bruins avenged last year's shocker in
With just 65 yards rushing, the Bruins leaned heavily on Cowan's untested arm. He completed eight of his first nine and went 20-for-29 for 201 yards in the game.
A sophomore who competed with Olson for the starting job before the season began, Cowan made a single brief appearance last year and had not attempted a pass until Saturday.
Austin, a senior seeing his first action of the season, was 15-for-30 for 192 yards passing.
Cowan and the Bruins answered immediately, with a touchdown pass to Willis that completed a three-play, 49-yard drive.
Justin Medlock kicked field goals of 33 and 39 yards for UCLA in the third quarter.
The Bruin defense held
UCLA now faces its toughest two-game stretch of the season, going on the road to play No. 11 Oregon and No. 12 Notre Dame in the Bruins' first games against ranked opponents.