Leading by six with under five minutes to play, Saint Joseph's saw its lead evaporate with 17 seconds remaining as a pair of free throws by Duquesne's Raegan Moore tied the game at 59-59.
With the final seconds ticking away, the Hawks worked the ball to Cloud on the right wing. Getting a step on her defender, Cloud drove the right wing and hit the go-ahead layup to put SJU up 61-59 with 3.9 seconds to go.
Duquesne (16-10, 8-5 A-10) had one final shot, but a desperation three-pointer by Moore was off the mark at the buzzer.
In a tight first half, Saint Joseph's used an 11-4 run to take a 30-24 lead into the half as Andrews scored her 14th point on a layup at the buzzer.
Saint Joseph's would push its lead to eight six times in the second period, but Duquesne pushed back each time leading to the thrilling final seconds.
For the game, the Hawks shot 49.1 percent overall (27-of-55), but hit just 2-of-6 from three-point range and 5-of-9 from the foul line. Despite being outrebounded 38-25, the Hawks scored 20 points off Duquesne turnovers and outscored the Dukes 36-18 in the paint.
Andrews finished the game 9-of-15 from the floor, including 1-of-1 from three-point range and 2-of-3 from the foul line to go with six rebounds and two assists. Redshirt junior Ashley Robinson had 13 points, eight coming in the second half, while Cloud finished with seven points and a team-high nine assists and seven rebounds.
Moore led two Dukes in double figures with 19 points as Duquesne shot 37.5 percent overall (18-of-48), 27.3 percent from behind the arc (3-of-11) and hit 20-of-24 from the foul line (83.3 percent).
Saint Joseph's returns to action Sunday at Dayton. Game time is set for 1 p.m. with the game airing nationally on ESPNU.