Conference player of the year Andrew Nicholson added 19 points for the fourth-seeded Bonnies (19-11), who are now a win away from advancing to the NCAA tournament for the first time since 2000.
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The Bonnies will face third-seeded Xavier for the championship and the automatic bid to the show on Sunday. The Musketeers (21-11) knocked off Saint Louis 71-64.
Massachusetts (22-11) rallied from a 16-point deficit with 7:29 to play and had a chance to take the lead in the closing seconds, only to see Raphiael Putney's high-arcing 3-pointer hit off the side of the rim with less than 2 seconds to play.
Matthew Wright hit two free throws to ice the game.
Terrell Vinson had 20 for UMass, which knocked off top-seeded Temple on Friday.