After struggling with the younger Dukes' quickness for much of the game, UMass (14-15) pulled away behind Mack's five 3-pointers in the second half, and the inside play of Lari Ketner, who scored 18 points and grabbed 11 rebounds.
UMass advances to play Xavier Thursday.
Courtney Wallace scored a career-high 26 points and pulled down seven rebounds for Duquesne (5-23), including two straight layups that helped the Dukes close to 55-53 with seven minutes left in the game.
Mack responded with a 3-pointer on the Minutemen's next possession for UMass, and Duquesne lost its offensive leader with 1:31 remaining when Wallace fouled out of the game.
Mack finished the game with 10-of-16 shooting from the field.
Duquesne came into the afternoon 1-19 in its last 20 games, with its last six losses coming by an average of 14 points.
But the Dukes, who started two freshmen and two sophomores, hung around the more experienced Minutemen behind Wallace's athleticism.
Wallace's 15 first-half points single-handedly rallied Duquesne from a seven-point deficit midway through the first period. A Mack layup after Chris Kirkland stole an inbounds pass gave the Minutemen a 21-14 lead.
Wallace then scored the team's last 11 points before halftime, including a one-handed reverse scoop shot off a baseline drive past several defenders.
Ketner scored 10 of his points in the first half, but the senior center turned the ball over three times and lost the basketball several more times while being double-teamed in the post by the Dukes.
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