Seth Berger and Donte Clark scored 15 points each and Antwan Space added 12 points and nine rebounds for the Minutemen (8-5). UMass outrebounded the Explorers 47-31 and had 15 on the offensive boards.
Jordan Price scored 23 points for the short-handed Explorers, who played just six players. Tony Washington added 11 points and 10 rebounds and Cleon Roberts also scored 11. La Salle (4-7) has lost six straight.
Antwan Space hit a 3 to break a 55-all tie with under 10 minutes left and UMass gradually built an eight-point lead. The lead was five when Space's dunk with 26 seconds left finished the scoring.
Davis hit a 3-pointer with three seconds left in the first half to cap a 12-2 run that gave UMass a 42-40 lead at the break.