The Wolverines (22-7, 14-3 Big Ten) were 16 of 23 from 3-point range, including Stauskas' career-high seven makes.
Michigan had the game in hand by halftime with a 52-30 lead. The Wolverines hit five straight 3-pointers midway through the half to break the game open. The 15-point run widened Michigan's 20-17 lead to a comfortable 32-17.
Almost lost in the shooting was a quietly dominant performance on the boards by the Wolverines, outrebounding Illinois 33-23. Jon Horford led Michigan with 10 boards.
The Illini (17-13, 6-11) had won three straight. The loss was their worst at home in the 51-year history of the arena formerly known as the Assembly Hall and now called the State Farm Center.
While Michigan broke 50 points by halftime, Illinois didn't get there until the game had just over three minutes left and had long been decided.
Michigan headed to the locker room the overpowering 22-point lead on a team that hadn't given up 50 points in any of its previous four games.
Offensively, the Illini weren't bad over those first 20 minutes, shooting 54.2 percent.
But the Wolverines were unstoppable. They were 11-for-14 from 3-point range (78.6 percent) in the first half.
In all, they hit 19 of their 28 shots from the field, a 68 percent pace that Illinois couldn't match.
Michigan had a dozen assists in those decisive 20 minutes and, against a team that had been living off steals, had turned the ball over just three times. The Illini had scored 20.7 points a game off steals during their three-game win streak.
It was the 3-pointers, though, that broke the game open.
Midway through the half, the Wolverines were good from 3-point range on five straight possessions. That turned a tight 17-13 game with 13:21 to play into a 32-17 blowout-in-the-making with just over eight minutes in the half.
As the clock wound down on the half, the Illini seemed determined to at least not let the Wolverines break 50.
Michigan had the ball and a 49-30 lead with 29 seconds left. Illinois committed three straight fouls to keep the Wolverines away from the basket.
Finally, with four seconds left, the Canadian Stauskas waited for the inbound pass from Derrick Walton Jr., as the Orange Krush student section aimed loud "USA! USA!" chants in his direction.
Stauskas took the pass and, just ahead of the buzzer, launched yet another 3-pointer. It slipped through the net and he enjoyed a long, slow stare at the student section before heading to the locker room.