Tomislav Ivisic had 14 points and 11 rebounds and Keaton Wagler chipped in with 14 points for the Fighting Illini (26-8), who advanced to face South Region No. 2 seed Houston, an 88-57 winner over Texas A&M.
Underwood celebrated after the game by waving both arms up in the air simultaneously at the Illinois crowd.
Illinois, which had a huge height advantage, held VCU to 35% shooting and outrebounded the Rams 45-29. The Illini blocked five shots.
Terrence Hill Jr. had 17 points for VCU (28-8).
VCU's Nyk Lewis went down for the game with a sprained right ankle in the opening minute and Illinois bolted to 20-8 lead.
But just as they did on Thursday night against No. 6 seed North Carolina, when they came storming back from a 19-point, second-half deficit to win 82-78 in overtime, the Rams got back in it with a series of 3-pointers to take a 28-26 lead behind 12 first-half points from Hill.
But VCU couldn't sustain the momentum.
Illinois took control late in the first half with Stojakovic scoring all nine points during a 9-0 stretch to close the half.
The second half was all Illinois.
The Illini pushed their lead to 17 early in the second half after VCU turnovers led to a high-flying transition dunk from Zvonimir Ivisic and Kylan Boswell's 3 from the top of the key to beat the shot clock.
The lead got to 23 with 4 minutes remaining, setting off a celebration among Illinois fans.
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Illinois is 3-2 all-time against Houston, but the Cougars won the most recent meeting 68-53 victory in the second round of the 2022 NCAA Tournament.
ABC7 Chicago contributed to this report.