Raymond Sykes and K.C. Rivers added 14 points apiece for Clemson (8-0), which overcame a 40-32 halftime deficit to earn their fifth consecutive win in the challenge.
Clemson turned the tables on defensive-minded Illinois (6-1) by causing havoc in the backcourt with a full court press, forcing 17 turnovers.
"We're very pleased to get out of here with a hard fought win," said Clemson head coach Oliver Purnell. "Our pressure had a cumulative effect and as the game wore on it wore them down. Our press is high risk, high reward."
The final lead change came following a free throw by Stitt that put Clemson ahead 68-67 with 4:31 remaining.
Stitt went to the free throw line with 11.1 seconds left, but missed the front end of a one-and-one, giving Illinois an opportunity to win or send the game into overtime. But Clemson's defense didn't allow the Illini to get a shot off as time expired.
"We made a decision to run and push it if they missed the free throw," said Illinois head coach Bruce Weber. "They had the momentum and I wanted to go for it. It's disappointing though because I would have liked to get a shot off to give us a chance."
Mike Davis led Illinois with a career high 28 points, including the first 12 for the Illini after the break. Demetri McCamey added 20 for Illinois, which has lost the three games they've played in the ACC/Big Ten Challenge.
Illinois shot 56 percent in the first half but fatigue took a toll as the Illini went cold down the stretch, going 2-for-8 from the field in the final five minutes.
"We did a great job defensively," Purnell said. "We did the kinds of things we had to do to win down the stretch in the last six to eight minutes. We got good shots and didn't turn the ball over."
Clemson went on a 9-2 run to take a 23-20 lead midway through the first half.
Davis brought the Illini back to life with a thunderous two-handed dunk on a fast break that sparked a 20-9 run.
Illinois led 40-32 at intermission. But the Tigers clawed back by scoring the first seven points of the second half.
Despite being outrebounded 35-23, the Tigers held a 56-26 advantage in scoring in the paint as a result of running the floor and getting in the lane for transition baskets.