Hassan Adams added 13 points, six assists and six rebounds for the Wildcats (15-3l, 5-1 Pac-10), who beat the Ducks (11-4, 3-3) for the fifth straight time.
Stoudamire was almost perfect in the first half, scoring 20 points on 5-of-8 shooting. He made all three of his 3-point attempts and was 7-for-7 from the free-throw line.
Bryce Taylor led Oregon with 20 points, and Aaron Brooks added 15 points and six assists.
Stoudamire ignited a game-turning 16-0 run when he made a pair of 3-pointers midway through the first half to give the Wildcats a 23-20 lead.
He scored four more points on free throws during that run, while Adams scored the other six points. The result was a 33-20 lead at the 6:28 mark. It was an advantage that held until halftime as Arizona led 42-29 at the break.
Stoudamire's fifth 3-pointer of the game put the Wildcats up 54-39, their largest lead of the game.
The Ducks, led by Brooks, answered with a 15-2 run to pull within two points, 56-54, with 8:27 left. Brooks scored the first seven points of the run and assisted on a two other field goals.
Mustafa Shakur gave the Wildcats some cushion with a jumper, followed by a 3-pointer for a 62-56 lead. After Ray Schafer made a pair of free throws to pull the Ducks back to within 64-61 with 4:25 to play, Arizona finished on a 10-5 run to close out the game.