The Illini (14-2, 1-1 Big Ten) led 37-25 at halftime and used a 13-2 run early in the second half to build a 50-27 lead.
Illinois used stingy defense to shut down the Buckeyes (11-3, 1-1), who shot just 33 percent from the field and turned the ball over 16 times.
Deshaun Thomas led Ohio State with 24 points, but beyond him the Buckeyes had no one to turn to for offense. Aaron Craft had a quiet 11 points and Lenzelle Smith Jr. finished with eight, all in the first half.
And while the Buckeyes searched for offense, the Illini got double-figure production from four players. Sophomore center Nnanna Egwu had 16 points and a game-high eight rebounds for the Illini point guard Tracy Abrams added 13 points and five assists, while reserve Joseph Bertrand scored 12 points.
Illinois came into the game off a stunning 68-61 loss at Purdue in its Big Ten opener, and had lost two of its last three over a stretch in which the team struggled to get stops. But on Saturday, Illinois became the first team to hold the Buckeyes under 30 points in the first half this season, taking a 37-25 lead.
The efforts of Illini big men Egwu, Sam McLaurin and Tyler Griffey were a big part of that success. Ohio State had just 10 points in the paint in the first half.
Illinois added to its edge early in the second half with a 13-2 run. Bertrand finished it, driving to the basket and hitting a short jumper as the shot clock wound down for a 50-27 lead with 15:05 to play.
The Buckeyes scratched their way back within 60-46 with 6:37 left on a jumper by Thomas. It capped a 15-4 run that melted what had been a 25-point deficit at 56-31 and put the sellout crowd -- still uneasy about just how good Illinois might be -- on edge.
But Richardson answered Thomas' shot with a 3-pointer with 6:13 to play. That put the Illini up 63-46 and let the crowd roar with relief.
Paul followed that with two free throws and Egwu added a dunk that pushed the lead to 67-46 with 4:52 to play, and Ohio State was all but finished.
The offensive production from Paul was no surprise. He came into the game averaging a team-high 18.5 points a game. But Egwu's big game was out of the blue.
The 6-foot-11 sophomore came into the game averaging 6.0 points and had never scored more than 12.
Illinois opened up a 14-point lead midway through the first half, using a 12-2 run and taking advantage of poor shooting by the Buckeyes. Bertrand capped it with a jump shot in the paint for a 25-11 lead with 10:08 to play that charged up what had been a quiet crowd.
Ohio State hit just 22 percent of its shots over the game's first 12 minutes, and the combination of turnovers and cold shooting cost them a chance to close the gap.
At one point Illinois missed eight straight shots, but Ohio State couldn't do much with the opportunity, going more than 3 minutes without a basket.