Carter's lone basketball of the game came off a pass from point guard Chaz Williams, who penetrated to the basket with less than five seconds remaining and kicked it out to Carter standing alone in the left corner.
Harvard, which had no timeouts remaining, was forced to jack up a desperation shot at the buzzer that landed well short.
Williams finished with 12 points and a game-high 10 assists for UMass, which was paced by junior guard Jesse Morgan's 19 points.
Trailing 64-61 with 1:21 remaining, Morgan made consecutive baskets -- a jumper and then a 3-pointer -- to tie the contest, 64-64, with 39 seconds to go.
The Minutemen got a chance to win after Williams forced a turnover by Harvard's Christian Webster with 28 seconds to go
Sophomore Wesley Saunders netted a game-high 18 points for Harvard, which trailed by as much as 10 points in the first half. Saunders went 10-for-11 from the free throw line, while freshman guard Siyani Chambers added 14 points.
Junior forward Raphiael Putney tallied 13 points for UMass, which also got a nine-point, 13-rebound performance from Cady Lalane.