C.J. Bryce added 17 points for the Seahawks (14-5, 6-2) who entered the game in a four-way tie for first in the Colonial Athletic Association standings.
Trailing 37-32 at halftime, Ingram hit back-to-back 3-pointers and the Seahawks rallied to a 48-45 second-half lead.
Rashann London's 3-pointer pulled the Dragons within 62-61 with 3:53 left, but Bryce scored five straight points and the Seahawks led 72-66 after Flemmings' 3 with 1:30 to go.
Kazembe Abif's layup and free throw pulled Drexel within 75-71, but Flemmings' layup with three seconds left iced it.
Rodney Williams scored 17 points and Abif added 14 for Drexel (3-16, 1-7), which has lost four straight.
The Seahawks outrebounded the Dragons 43-29 and outscored them 38-22 in the paint.