Malcolm Duvivier added 15 points for the Beavers (15-7, 6-4 Pac-12 Conference), who improved to 13-0 at Gill Coliseum this season.
Neither team was able to pull away until the Beavers went on an 8-0 run, with Reid's jumper putting Oregon State up 51-44 with 2 minutes 27 seconds left.
The Cougars (10-12, 4-6) trimmed the lead to four points, but Reid's driving layup with 47 seconds left made the score 53-47 and helped seal the win.
Josh Hawkinson had 16 points, 10 rebounds and three steals and Ike Iroegbu scored 11 for the Cougars. Washington State outrebounded Oregon State, 43-34, but had 12 turnovers compared to the Beavers' five. Both teams shot poorly, with the Cougars hitting 37.3% and the Beavers shooting 38.9%.