Butler took a four-point lead with 3:11 remaining and allowed the Hawks just two points the rest of the way in what was the opener of both teams' Atlantic-10 Conference campaign.
Clarke gave Butler a 57-56 advantage with a 3-pointer after the Hawks had led for much of the contest. He delivered 28 points, hitting six 3-pointers along the way. Andrew Smith added 24 points and 10 rebounds for the Bulldogs (13-2), who overcame a five-point halftime deficit.
Chris Wilson had 15 points for St. Joseph's.