Nunn scored 13 on 4-of-6 shooting for the Illini (16-12, 5-10 Big Ten). He was 3 of 4 from 3-point range. Hill added 10 points and five rebounds.
Nebraska (16-11, 8-7) came into the game as one of the Big Ten's hottest teams. The Cornhuskers had won seven of their last eight.
But Nebraska turned the ball over 15 times and was 0-8 from 3-point range in the first half before finishing 3-13.
Only one Cornhusker, Terran Petteway, finished in double figures. He had 13 points.
Rayvonte Rice added 10 point and nine rebounds for the Illini. Illinois was just looking to win back-to-back games for the first time since the opening week of the conference season. The Illini opened Big Ten play 2-0 but had dropped 10 of 12 since then.
Over a stretch of just a minute midway through the second half, Illinois turned what had been a tight game into a comfortable contest, opening up a 13-point lead.
It started and ended with buckets by Jon Ekey.
With 10:48 to play the forward sank a 3-pointer, giving the Illini a 46-37 lead.
At the other end, Rice stole the ball from Shavon Shields, broke to the basket and hit a layup.
He was fouled and missed his free throw, but the Illini got the rebound and with 9:49 to play Ekey tipped a ball in that put the Illini up 50-37.
The Cornhuskers could get no closer than eight over the final nine minutes, getting there twice. Both were on layups by Petteway, with 8:13 to play and again with 2:23 left.
Both teams suffered through stretches of frustrating shooting and ball handling.
The Cornhuskers had the worst of it.
They usually hit a solid 34.3 percent of their 3-point shots but their 0 for 8 first half was the biggest reason they were behind at the break, 27-24.
Petteway came in with four straight 20-point games but the Illini shut him down until late. He had just two points in the first half.
And Illinois had something to do with the 15 Nebraska turnovers. Illinois had 11 steals, four of them by Rice.