It was the Hawks' first win over a ranked team since beating No. 20 Notre Dame, 79-70, in overtime on Nov. 16, 2012.
This week, the Hawks will host the A-10's top two teams: St. Louis on Wednesday and Virginia Commonwealth on Saturday. A successful week would clearly put the Hawks in the NCAA tournament conversation.
St. Joe's received 48 points from its starting frontcourt: 18 from Halil Kanacevic, 17 from Ronald Roberts Jr., and 13 from DeAndre' Bembry.
Point guard Chris Wilson scored 12 points. He has scored in double figures in five of the last six games. Leading scorer Langston Galloway, who was saddled with foul trouble, scored a season-low seven points.
UMass was led by Derrick Gordon, who scored 21 points. Point guard Chaz Williams, who had 22 points in UMass' 66-62 win over the Hawks on Jan. 8, scored 13 of his 16 points in the second half.
On Saturday, St. Joseph's led by as many as 17 points and owned a 41-25 halftime lead.
"Sometimes you have to find a way," Wilson said. "It is going to be ugly, and we're mad about giving up the lead, but either way it goes in the same column."
In the second half, UMass showed greater intensity on defense.
"It was gutty, and we did what we had to do to win a game, but I am concerned about our offense," said St. Joseph's coach Phil Martelli, whose team shot 21 of 51 from the field and 25 of 40 from the foul line.
UMass tied the score twice late in the game, the second time when Williams hit the first of two free throws to tie it at 68 with 39.2 seconds left.
Williams missed the next foul shot, and UMass failed on three put-back attempts.
Wilson then hit two free throws for a 70-68 lead with 30.1 seconds remaining.
The Hawks' Papa Ndao then stole the ball as one of the Minutemen drove the baseline. Ndao was fouled and made both free throws with 12.6 seconds remaining, and the Hawks survived.