Kendall Anthony sparked the surprising result by hitting four 3-pointers and scoring 21 points.
Richmond led by five at halftime and although the Minutemen tied the game early in the second period they could never move in front.
A jump shot by Trey Davis with 13 seconds to go cut the Massachusetts deficit to 56-55 and Lindsay then hit two free throws to account for the final score. Chaz Williams could not connect on his 3-point attempt in the final moments.
Lindsay added 11 points for Richmond (13-6, 3-1 Atlantic-10 Conference).
Massachusetts (16-2, 3-1 A-10) had a six-game winning streak snapped. Sampson Carter paced the Minutemen with 15 points.