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.
Reserve center Akolda Manyang has been charged with felony aggravated assault after being accused of punching a man in the face without provocation.
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ESPN college basketball reporter Andy Katz discusses the need for the Pac-12 putting in place rules on that would prohibit storming the court after a win.