The victory avenged a 55-54 overtime loss in Tempe on Jan. 2.
Washburn had 19 points, 18 rebounds, and four blocks in the first game.
His reverse layup put Utah ahead 54-53 late, then two free throws with 25 seconds remaining helped seal Wednesday's victory.
Carrick Felix led ASU with 14 points and 11 rebounds. Jahii Carson added 12 points but was called for a charge with 17 seconds left and the Sun Devils down by three.
Jared DuBois' ensuing free throws provided the final margin.
The Devils led 49-41 with 7:17 remaining but were outscored 19-6 the rest of the way.
ASU trailed 29-22 at halftime, tying its lowest first-half output.