Stoudamire, who had 23 points in the first half, hit six three-point shots as Arizona (12-3 overall, 2-1) won its 14th in a row against the Cardinal.
Dion Cross led Stanford (11-2, 2-2) with 25 points, but had only seven after the first half.
Stoudamire finished one point shy of the Arizona single-game scoring record of 46 by Ernie McCray in the 1959-60 season.
Stoudamire had nine points during a 24-6 run by the Wildcats midway through the second half that wiped out an 11-point Stanford lead and gave Arizona a 70-63 lead.
But the Cardinal, behind six points from Brevin Knight and five from Andy Poppink, rallied to tie the game with 40 seconds left at 76-76 on a layup by Knight.
Arizona then ran down the clock and Stoudamire drove to the basket, but his shot was blocked by Bart Lammersen with six seconds left. Stanford missed two shots in the final seconds of regulation.
No. 12 Arizona State 73, No. 20 California 68--For Arizona State Coach Bill Frieder, the three-day road trips common during the Pac-10 basketball season can destroy a team--especially if it plays poorly in the first game.
But the Sun Devils (12-3, 2-1) rebounded from a 16-point loss just two days earlier by beating the Golden Bears (8-4, 1-3) in Oakland as Mario Bennett had 20 points and the team made 16 steals.
"This is really huge," Frieder said. "The toughest thing to do on the road is win Saturday afternoon after you've lost Thursday night. It's huge."
Bennett, who had six dunks, added five blocks and three steals for Arizona State, which lost, 91-75, at Stanford on Thursday.
The Sun Devils' full-court press led to 24 turnovers by the Bears and several fast-break baskets for Arizona State.
Tremaine Fowlkes had 17 of his 23 points in the second half for Cal, which has lost four of five.
Williams scored 13 points in the first half as the Ducks built a 45-35 lead. Oregon then opened the second half with a 12-5 run to increase its advantage to 57-40. Oregon State could get no closer than 13 afterward.