Dunham went 6-of-9 from 3-point range en route to a 32-point performance, with Marshall amassing 30 points on 12-of-18 shooting to help the Bulldogs move to 5-0 under first-year head coach Brandon Miller.
Butler's win sets up a matchup with fifth-ranked Oklahoma State on Friday. The Cowboys topped Purdue by an 97-87 count in the tournament's opener.
Washington State (2-3) was dealt a third straight defeat following a 2-0 start despite 26 points from DaVonte Lacy. Que Johnson finished with 11 points in the setback.
The Cougars held a 65-62 lead following Dexter Kernich-Drew's 3-pointer with around 3 1/2 minutes left, but Dunham knocked down a triple on the ensuing possession to knot the score. The basket ignited a 14-4 Butler run to close out the contest, during which Dunham sank two more baskets from beyond the arc.
Dunham's last three of the day put the Bulldogs up 73-67 with 54 seconds remaining. After Washington State's Ike Iroegbu misfired on the other end, Dunham hit a pair of free throws to put the game out of reach.
Butler owned a slim 30-26 edge at the half, but Lacy netted all nine points of a 9-4 Cougars' burst to begin the second period that staked Washington State to a 35-34 advantage.