Clarke scored 12 points in the first 11 minutes of the second half. The Bulldogs (18-4, 5-2 Atlantic 10) trailed 32-30 at the break, then went on a 15-3 run.
Nikola Malesevic led Rhode Island (6-14, 1-6) with 18 points in the Rams' fourth straight loss.
Butler began the game looking like the team that lost 75-58 at Saint Louis early in the week. The Bulldogs went down 25-16 in the first half—their largest deficit of the game.
Marshall scored 10 of the Bulldogs' first 14 points, getting the majority of his points off hustle plays and high-flying dunks. Marshall finished with 13 points, despite only playing nine minutes in the second half.
The Bulldogs came storming out to start the second half, looking like the team that has beat three top-10 teams this season. They held Rhode Island without a field goal until the 13:24 mark of the half.
Jones helped Clarke set the tone throughout the opening run in the second half for Butler. He scored nine of the points in the swing.
The Rams hung around. The Butler lead swelled to 67-54 with about 4 1/2 half minutes to play, but Rams fought back forcing a turnover and grabbing two steals.
A field goal by Malasevic brought the Butler lead down 70-66 with about a minute and a half to play, but two free throws from Jones sealed the game for the Bulldogs,