Azotam hit 8 of 9 from the field while Shannon matched his season high for points and handed out six assists off the Bobcats' bench. Ousmane Drame added 12 points and nine rebounds while Evan Conti had 11 points for Quinnipiac (10-13, 6-5).
The Bobcats shot 58.6 percent (34-58) from the field and 6 of 14 from 3-point range, with 22 assists to seven for Monmouth.
Monmouth shot just 41.1 percent (23 of 56), though it did made 12 of 14 at the foul line.
Quinnipiac opened with an 11-0 run in the first 3 minutes and rolled from there.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.