Clarke also had a rebound and an assist, while he shot 50 percent from behind the arc and 45 percent from the floor.
The Bulldogs improved to 14-0 when junior forward Khyle Marshall scores more than 10 points. Marshall finished the night with 14 points, two rebounds and two steals.
"It was good for me to see him have that success," Butler coach Brad Stevens said in a release. "I like the fact that we got him the ball and I like what he can with that ball. Khyle has always risen to the occasion as the season has progressed."
Butler's swarming defense gave the Dukes problems all game long, holding them to 37 percent shooting from the field and a mere 23 percent from behind the arc.
"I think collectively we're guarding better," Marshall said. "We held a great three-point shooting team to only 49 points so I think that's a pretty big accomplishment on our part."
The Bulldogs took advantage of their size advantage inside and out-rebounded the Dukes 36-28. Senior center Andrew Smith led the team with 10 rebounds and sophomore forward Roosevelt Jones added eight.
"Our guys were really locked in defensively and I thought we played at a much better pace offensively. " Stevens said.
Freshman guard Kellen Dunham came off the bench in the first half to score eight points in 83 seconds. He finished the game with 11 points and made three of his five shots from behind the arc.
Butler will host Saint Louis on Friday at 7 p.m. (ESPNU).