Azotam added nine rebounds and Shannon chipped in seven boards and seven assists to keep Quinnipiac (14-13, 10-5) undefeated for the month of February.
Tied 13-all with 8:29 left in the first half, the Bobcats closed out the period on a 14-6 run sparked by consecutive baskets from Azotam. Quinnipiac led at halftime 27-19.
Bryant got within four points in the second half, 58-54, behind Corey Maynard's layup with 4:11 to play, but the Bobcats answered with six straight points to take a 64-54 lead with just under two minutes remaining.
Quinnipiac made seven free throws in the final two minutes to put away the game.
The Bobcats outrebounded the Bulldogs 43-30, and outscored their bench 31-9.
Frankie Dobbs led Bryant (17-9, 10-5) with 15 points.
The Cavaliers bring in a top-10 class of four incoming freshmen, so the Class of 2017 will be a small one. Coach Tony Bennett is aiming high.
College basketball coaches across the country will hit the recruiting trail hard in July to target the Class of 2017's top prospects. Which players are the nation's top programs targeting?
Wendell Carter, the No. 2-ranked player in the 2017 class, skipped a basketball event for a school play. And he's seriously considering Harvard.