Jordan Bachynski added 12 points for the Sun Devils (20-7, 9-5 Pac-12).
Arizona State finished the first half with a 14-3 run to lead 36-22 at the break and was up by as many as 21 before Washington State cut it to eight in the late going.
The Sun Devils, one of the worst free-throw shooting teams in the country this season, sealed the win with eight straight in the final 1:35.
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Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.