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.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.