Damyean Dotson and Carlos Emory scored 14 points apiece for Oregon (14-2, 3-0 Pac-12), and Dominic Artis added 10.
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Jahii Carson scored 20 points, and Evan Gordon had 17 for the Sun Devils (14-3, 3-1).
Carson's potential game-tying 3-pointer at the buzzer was wide.
A 3-pointer by Felix with 2:08 to play put Arizona State up 60-59, but Woods answered for the Ducks with a two-handed slam to give Oregon a 61-60 advantage with 1:44 remaining.
Oregon went 7 of 8 from the free-throw line in the final minute to seal the win.
The Ducks used a 7-2 run in the final 3 minutes of the first half to lead 32-28 at halftime.