With the Eagles trailing 47-46, Leola Spotwood stole the ball and then Craig scored.
After a timeout by the Hawks, Crystal Whittington blocked a game-winning shot attempt by Kwinnyata Mercer with four seconds to play.
The Eagles (17-11, 12-3 MEAC) survived despite shooting just 28.3 percent from the field.
Whittington led Coppin State with nine points and nine rebounds.
UMES (10-17, 7-8) was led by Chelsea Sanders and Mercer, who each had 14 points.
Craig converted two free throws with 1:16 to play to cut the UMES lead to 47-46 and then added her game-winning layup to give the Eagles their 15th victory in the past 17 games.
Delaware State 67, Morgan State 60, OT: Redshirt freshman Tierra Hawkins, the twin sister of Maryland junior Tianna Hawkins, led all scorers with 18 points and 14 rebounds as the host Hornets defeated the Bears for the second time this season and earned the tiebreaker over them for MEAC tournament seeding.
With just over 10 minutes remaining in the game, Morgan State (6-22, 3-12 MEAC) held an 11-point lead before Delaware State (6-22, 3-12) rallied.
The Bears were led in scoring by Dekisha Mathis' 16 points.
Earlier Monday, Hawkins was named MEAC Rookie of the Week for the third time this season.
Central Connecticut State 72, Mount St. Mary's 68: The host Blue Devils used a big run to take the lead in the first half and held on after a couple of comeback attempts to spoil the Mount's hopes of hosting a home game or notching a higher seed in the Northeastern Conference tournament.
Jessie Kaufman paced the Mount (14-15, 10-8 NEC) with 19 points. Selina Mann posted 12 points, eight rebounds, seven assists and five steals.
Jaclyn Babe led the Blue Devils (13-16, 7-11) with 19 points.
Morgan State 73, Delaware State 72: Aric Brooks sank two technical free throws with 1.1 seconds left to give the visiting Bears (8-19, 4-10 MEAC) a one-point win over the Hornets (14-13, 11-4) in a bizarre finish.
The Hornets appeared to win the game, 72-71, on a follow-up slam by Tahj Tate with 0.4 of a second showing on the clock, prompting fans to storm the court.
After a conference, the officials accessed a technical foul on Delaware State for delay of game and reset the game clock to 1.1 seconds.
Blake Bozeman was the top scorer for Morgan State with 14 points.
Coppin State 64, UMES 60: Antonio Williams scored 11 of his 15 points in the second half to help the Eagles (14-14, 9-6 MEAC) overcome a seven-point halftime deficit on their way to a victory over the host Hawks (7-21, 4-10).
Williams finished the game with 15 points and 15 rebounds to lead the Eagles to a season sweep of UMES.