Three Spartans scored in double-figures led by Drew Neitzel's 19. Goran Suton added 15 and Raymar Morgan chipped in with 10.
Neitzel made a key jumper with less than a minute left to seal the victory for MSU.
Rich McBride scored 12 points for the Fighting Illini (13-6, 1-3), who led by as many as 14 points in the first half. Warren Carter scored 11 points and Shaun Pruitt added 10.
Illinois led 34-23 at halftime after a dominant performance by McBride, who hit three consecutive three-pointers to lift Illinois.
After trading baskets to open the second half, MSU went on an 11-0 run to tie the game at 36 with 14:16 left.
"It was a tale of two different halves," said Coach Tom Izzo. "At halftime, I don't know what kind of speech it was, but I said I was tired of being shorthanded, and not pressuring. I said we just need to leave it out there even if guys are laying on the floor, we need to leave it all out on the floor," he added.
McBride answered with a three-pointer to put the Fighting Illini up by three, but they would not score another basket for the next seven minutes.
With Illinois leading 39-36, the Spartans went on an impressive 15-0 run to send the home crowd at the Breslin Center into a screaming frenzy.
"It was a heroic effort by our team, I thought, in the second half," said Izzo.
MSU improved to 13-0 at home this season, holding their opponents, including Illinois, to just 57.1 points per game.
Warren Carter broke the MSU run with a three-pointer.
"Our kids were very focused, things were going their way," said Illinois Coach Bruce Weber. "And then the second half, their pressure, their intensity. The crowd got into it. We just kind of froze like deer in the headlights. The first few possessions we just turned it over and then the crowd got into it and they got some layups," he added.
Illinois was down 57-50 with 2:50 left when Chester Frazier scored a tough layup. He then followed with a steal from Travis Walton on the inbounds and hit an acrobatic layup to pull his team within three with 2:25 left.
Goran Suton answered with a jumper at the other end and put the Spartans up by five.
Shaun Pruitt pulled the Illini back within three at 59-56 with 53 seconds remaining, but Drew Neitzel sealed the win with a jumper with 25 seconds remaining to make it a two-possession game.
Michigan State earned their biggest win of the season, not only coming back from a large deficit, but also beating a team that has dominated them in recent years.
The Spartans now have a week off until their next game at Penn State on Saturday afternoon.