The Big Ten tournament champions were led by their star duo of Kofi Cockburn, who scored 18 points and five rebounds and Ayo Dusunmu, adding 17 points, 11 rebounds and six assists.
Xavier Bell had 12 points for Drexel (12-8) and James Butler added 10 for the Dragons, who were held to 30.6 percent shooting from the field and committed 11 turnovers.
Illinois dominates Drexel in every area to rout the Dragons
Drexel held an early 8-7 lead after Bell sank a three-pointer, but that would be the last lead the Dragons would hold. Illinois rattled off 10 straight points, keyed by Cockburn, who scored six of the ten, his final two points came on a monster dunk.
The Dragons ended the stretch with a triple by Zach Walton. The Fighting Illini defense held Drexel to just one field goal over the final five minutes of the half and led 39-21 at the break, holding the Dragons to 21.6 percent from the floor.
Illinois started the second half on a 17-4 run to go in front 56-25 and they cruised past the CAA champs the rest of the way. The Fighting Illini outrebounded Drexel 40-32 and held a 58-16 advantage on points in the paint.
The Fighting Illini advance to the second round where they will face eighth seed and in-state rival Loyola-Chicago on Sunday.