The win gave head coach Bruiser Flint his 213th victory at Drexel, tying him with Sam Cozen for the most in program history.
Drexel (1-1) trailed 30-27 late in the first half but went on a 14-2 run that spanned into the second half to take a 41-32 lead. The Dragons shot 46.7 percent from the field while holding Illinois State (0-2) to just 32.3 percent.
Drexel was coming off a 72-67 loss on Saturday at then-No. 22 UCLA.
Michael Middlebrooks recorded his first career double-double for Illinois State, scoring 10 points and grabbing 15 rebounds.