Butler (27-8) heads into a third-round East Region game Saturday against No. 3 seeded Marquette, which barely escaped a upset at the hands of Davidson, 59-58 later Thursday.
Bucknell, with was seeded 11th, ends its season with a 28-6 record, although the 28 wins mark a school record.
With Bucknell suffering though 26 percent (7-of-27) first half shooting, the Bulldogs were able to have a 21-14 lead at half. Bucknell rallied in the second half and pulled ahead only to have Butler again turn up the defensive pressure. Bucknell managed just one field goal in a 7-minute span and ended up 23-of-62 (37.1 percent) shooting.
Butler posted a 14-2 run in that spell and built a 53-42 lead and held Bucknell off from there.
Clarke made just 5-of-14 shots from the field but was 5-of-6 from the free-throw line, helping the Bulldogs go 25-of-28 (89.3 percent) from the line as a team. Roosevelt Jones had 14 points while Andrew Smith chipped in 14 points and 16 rebounds.
Joe Willman, with a game-high 20 points, was the only Bucknell player in double figures.