Within the first six minutes of the second half, Drexel cut the lead to eight on two occasions but would never get any closer.
"The thing you can't do is get too far behind because even if you come back they will make a tough shot and they just throw it to some guy who scores," Drexel coach Bruiser Flint said.
The Blue Hens were led by guard Devon Saddler, who scored 23 points and added seven assists and eight rebounds.
Guard Jarvis Threatt had 18 points and nine assists for Delaware, which outrebounded the Dragons, 44-27.
"We made mistakes in the second half starting out, but we turned it around because we had a cushion," Threatt said.
Slowly, Drexel is returning to health, although dynamic scorer Damion Lee is out for the season and sophomore forward Kazembe Abif missed his fifth straight game. Both have knee injuries.
Sophomore forward Tavon Allen, who missed the last two games with an ankle injury, returned and brought his shooting touch. Allen scored 19 points off the bench, hitting 5 of 7 from beyond the arc.
Drexel also received a team-high 20 points from Frantz Massenat, who also had 10 assists. Chris Fouch scored 18 for the Dragons.
With 7 minutes, 5 seconds left and the Blue Hens leading by 72-55, Delaware's Davon Usher limped to the bench and did not return. He finished with 12 points. Coach Monte Ross said it appears to be a groin injury and hopes there is enough time for Usher to be ready for Saturday's showdown with other unbeaten team in CAA play, Towson.