Alleyne scored the last 10 points for Oregon and finished with 30 points and 25 rebounds.
The Bruins have won four in a row on the road in the Pac-12, dating back to last season.
Nirra Fields led UCLA with 19 points, but California used a 15-0 run to walk away with the victory.
The game will be televised live on the Pac-12 Networks and will air on AM 1150.
Nirra Fields led the Bruins with a game-high 22 points.