Joseph Bertrand pulled Illinois within 44-42 on a short jumper with 12:37 left.
But the physical matchup took its toll on the Illini (14-3, 1-2). And as Illinois piled up fouls, Trevor Mbakwe connected on layup with 6:15 to play for a 62-49 lead that Illinois couldn't overcome.
Mbakwe added 19 points and 11 rebounds.
Brandon Paul led Illinois with 21 points. D.J. Richardson and Tracy Abrams each scored 14.
After leading 34-30 at the half, the Gophers used a 50-point second half to surge to the win.
It started with an early 8-2 run that pushed the lead to 42-32.
While the Gophers were mostly plodding through the second half's first five minutes, Illinois struggled even more.
The Illini missed their first seven shots of the half and saw their shooting rate for the game drop briefly below 22 percent. They finished at just 34.5 percent and 12.5 percent from 3-point range.
At one point, with the shot clock ticking low, the Gophers fumbled with the ball and almost lost it near half court. Hollins finally scooped it up and heaved a desperate shot from halfcourt as the shot clock almost expired. The ball gently slid off the glass and in for a 3-pointer that made the score 42-30.
Illinois fought back within 44-42 with 9:37 to play when Bertrand pulled down a big defensive rebound, dribbled the length of the court and connected on a jump shot from inside the paint.
The crowd rose with the shot, sensing a comeback. But just as quickly as Illinois got back into the game, it fell back out.
Less than a minute after his shot and with Illinois down 46-42, Bertrand headed to the bench with his fourth foul.
Hollins made his free throws to put Minnesota back up by six, 48-42 with 11:54 to play.
Ten seconds later he hit a 3-pointer that extended that lead to 51-42.
Abrams, Bertrand and Nnanna Egwu each finished with four fouls, and Abrams and Bertrand both picked up theirs with more than nine minutes left in the game.
The physical tone was set early.
Paul went over Mbakwe just over three minutes into the game for a flying, right-handed dunk that left the Gopher forward on the floor.
Less than a minute later, Paul had to leave the floor, cupping a hand under a bloody nose after a foul by Austin Hollins. The senior guard spent the next five minutes on the bench with an ice pack on his nose and, finally, in the locker room.
The Illini survived that early stretch just fine. Richardson hit a long 3-pointer with 10:46 left in the half for a 16-11 lead just before Paul returned.
The Gophers felt the frustration.
Center Elliott Eliason headed to the bench a short time later after a foul he didn't think he committed only to be met by a sharp "Do your job!" from coach Tubby Smith.