Seth Gearhart had 14 points for Rice, including three 3-pointers.
Rice shot 30.8 percent, compared to 45 percent for Oregon State. The Beavers also out-rebounded the Owls 44-27.
Oregon State took a 14-4 lead with 11:44 left in the first half after a layup by Cheikh N'Diaye.
A Gearhart 3-pointer with about 7 minutes remaining in the half brought the Owls to within three points, 16-13.
Oregon State stretched its lead to as many as 12 before going into the half up 32-22.
Rice made it 37-35 on a 3-pointer by Dan Peera with 12:36 left before Oregon State responded with a 12-3 run.
Oregon State coach Wayne Tinkle led Montana to three NCAA Tournament appearances. He inherited an Oregon State squad that went 16-16 last season and lost several key players.
Oregon State's top returning scorer is Langston Morris-Walker, who averaged 4 points per game in 2013-14.
Reid's previous career high was 7 points, which he had surpassed before halftime.
Mike Rhoades, the new coach of the Owls, spent the last five seasons on the staff of Virginia Commonwealth University, where he was associate head coach.
Rice finished 7-23 last season and lost its top two scorers, but has three returning starters, including Max Guercy, who averaged 9.3 points per game last season.
Gary Payton II, a junior college transfer, had 6 points and 9 rebounds for Oregon State. His father is former Beaver All-American Gary Payton, who was inducted into the Pro Basketball Hall of Fame in 2013.