Boston (14-7, 7-1 Patriot League) led by 20 with 8 minutes to play but Bucknell went on a 28-9 run to cut its deficit to 59-58 on a 3-pointer by Chris Hass with 19 seconds left.
Papale then hit three of four free throws and Watson Jr. made a layup to help the Terriers seal the victory, their seventh in their last eight games.
Boston held Bucknell (9-10, 4-4) to just 16 points and 25 percent shooting in the first half. Bucknell shot only 33.3 percent from the field for the game but the Terriers didn't fare much better, making just 37.3 percent of their field goals.
Cameron Ayers scored 23 points and Hass added 17 for Bucknell.
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