Illinois (17-8, 5-5 Big Ten) rode a run of 3-pointers from Smith and Rich McBride to a 29-25 halftime lead that Minnesota never overcame.
Minnesota (9-14, 3-6 Big Ten) was led by junior Dan Coleman's 13 points.
For the game the Gophers shot 32 percent, and hit three of 18 3-pointers.
Illinois and Minnesota traded leads through the middle of the first half, and the Gophers pulled ahead 20-18 at 8:06 on a 3-point shot by sophomore Kevin Payton.
That was the last shot Minnesota made from the field until junior Limar Wilson's layup with less than a second left in the first half.
Before Wilson's bucket, the Gophers made 10 trips down the floor and came away with only two points, both on free throws by Lawrence McKenzie. Minnesota also failed to make an offensive rebounds over that stretch.
Another, scoreless run early in the second half doomed Minnesota.
The Gophers didn't score a point between Payton's free throw at 15:15 and another free throw by Payton at 11:00. By the end of that stretch the Illini led 48-31.
Minnesota made a run at the Illini, outscoring them 9-2 over a 3-minute span late in the second half to cut the lead to 56-45 with 2:45 left to play.
But Trent Meacham's long jumper from the baseline at 1:47 gave Illinois an 11-point cushion at 58-47.