Nigel Hayes had 14 points for the Badgers, who are now off to their best start in school history at 23-2. Wisconsin leads the Big Ten at 11-1 in conference play.
The Badgers took control of the game with a 20-4 run sandwiched around halftime as Illinois missed seven of its last eight shots to end the first half.
Wisconsin went up 40-26 when Hayes dived out of bounds to deflect a missed 3-pointer into Josh Gasser's hands. He found a wide-open Koenig for 3, and the Illini got no closer than nine points the rest of the way.
Illinois: The last time the Illini defeated a top-five team on the road was March 5, 1989, when Nick Anderson's 35-footer at the buzzer led Illinois past No. 3 Indiana 70-67. . Rice had averaged 21.5 points and nine rebounds in his games against Wisconsin last season.
Wisconsin: Gasser will need at least one more game to become only the second player in school history with 1,000 points, 500 rebounds and 250 assists. He came into Sunday needing 10 points to accomplish the feat but was held to three points on 1-of-5 shooting. Michael Finley finished his Wisconsin career with 2,147 points, 648 rebounds and 371 assists. Coach Bo Ryan received a standing ovation before the game for being selected as a finalist for the Basketball Hall of Fame.
Illinois hosts Michigan State on Feb. 22.
Wisconsin visits Penn State on Wednesday.