Jahii Carson added 23 points, six rebounds and six assists for the Sun Devils (17-6, 6-4 Pac-12), who had a chance to win at the end of regulation, then took the lead for good halfway through overtime.
Pac-12 scoring leader Roberto Nelson had 26 points, 24 after halftime, to lead the Beavers (13-9, 5-5) and scored with 19 seconds left in regulation to force overtime.
Jordan Bachynski added 17 points, 15 rebounds and seven blocked shots for the Sun Devils, who won their fourth in the last five games.
In overtime, Jonathan Gilling hit a 3-pointer - his first basket of the game - with 2:48 left and scored six straight to take a 78-72 lead with 1:27 left. Nelson hit a 3-pointer with three seconds left to get Oregon State within 84-82. Marshall made two free throws with 1.1 seconds left for the final margin.
After Arizona State opened up a seven-point lead midway through the second half, Oregon State ran off six straight points, the last four from Devon Collier underneath to tie it at 55 with 5:48 remaining. The Beavers got within 63-62 but failed to score on three straight possessions.
However, Jermaine Marshall missed one of two free throws with 27.8 seconds left and Nelson drove for a layup with 19.7 seconds to tie it at 64. Carson missed a jumper with two seconds left and the game went to overtime.
Oregon State opened up a 28-21 lead in the first half as the Sun Devils missed 16 of their first 22 shots.
Arizona State improved to 12-1 at home, while Oregon State fell to 2-6 on the road.
Nelson, averaging 21.8 points a game, was held to two points in first half, on 1-for-3 shooting over 10 minutes. He picked up two fouls and sat for the latter part of the half.
Oregon State held a 29-26 advantage at the break.
With seven blocks on Thursday, Bachynski has 279 in his career, passing Arizona's Anthony Cook for the conference career record of 278.
Arizona State was 5-of-20 from the floor at that point.