Austin Hollins had 17 points, five assists and four steals, Joe Coleman added 15 points and seven rebounds and the Gophers did most of their damage on the perimeter and the fast break to notch their largest winning margin this season.
Jordan Dykstra scored 17 points for the Jackrabbits (6-3), who missed Wolters their standout from nearby St. Cloud whose ankle injury prevented him from playing in his home state for the final time.
Minnesota is 16-0 against South Dakota State since the two schools first met in 1930. The Gophers play at USC on Saturday before wrapping up their nonconference schedule at home against North Dakota State and Lafayette.
They'll be challenged often in a Big Ten that's as top heavy as it's been since Smith arrived from Kentucky, far more than in these December games against mid-major foes.
But the Gophers will bring a deep, athletic team that's clearly growing in confidence.
Their defense, with Austin Hollins getting steals with his long, quick arms on the wing and Rodney Williams swatting shots around the basket, has never been in question.
Outside shooting and careful ball-handling have been perhaps the biggest concerns, and at least for this night the Gophers put all that to rest.
They turned the ball over only 13 times, compared to 21 assists, and shot nearly 57 percent from the floor.
Not to let the guards get all the attention, Trevor Mbakwe had eight points and 10 rebounds off the bench. The Gophers started the game by making 11 of their first 17 field goals and began to make this look like a dunk contest in the first half, grabbing nearly every loose ball and turning them into easy fast breaks.
Freshman Jake Bittle, who replaced Wolters in the starting lineup, had five points, seven assists and seven turnovers.
Bittle lost his dribble near midcourt when Austin Hollins and Elliott Eliason converged on him near the 5-minute mark, and Hollins took the ball the other way for an uncontested double-pump dunk to stretch Minnesota's lead to 30-18.
South Dakota State coach Scott Nagy lowered his head and buried it in his hands as soon as Bittle lost the ball. Andre Hollins followed with a 3-pointer on the next possession, off another steal by Austin Hollins.
Less than 30 seconds after the intermission, Williams zipped a kick-out pass to the wing for Austin Hollins, who swished another 3-pointer to put the Gophers ahead 51-24. They took their biggest advantage of the game, 59-28, a few minutes later.
The Jackrabbits have a 21-game winning streak on their home court, but this four-hour drive from their campus in Brookings was a long way from that comfort.
After their first NCAA tournament appearance last season, they've lost by three points each at Alabama and at Hofstra, both in the closing seconds.
Without Wolters, though, they sure missed a lot. The 6-foot-3 senior, who in 2011-12 became just the fifth player in NCAA history to average at least 20 points, five rebounds and five assists per game over a season, could only watch in his warm-ups.
Another key perimeter player, sophomore Taevaunn Prince sat out with an injury.