Tolzien finished 15 of 20 for 159 yards in his third career start and freshman Chris Borland flipped head over heels to block a punt as the Badgers turned a slow start into an easy win early in the second quarter.
But questions remain for Wisconsin (3-0) heading into the Big Ten Conference opener against Michigan State next Saturday. The Badgers fumbled six times, losing three of them, and their two heralded backs both had shaky performances.
Sophomore John Clay got the start after a career-best 143 yards against Fresno State last week, but finished with 70 yards on 12 carries and fumbled three times.
Brown, the previous starter, gained 63 yards on 12 carries and lost his only fumble. The junior joined Clay reaching 1,000 yards for his career with his 2-yard TD run late in the third quarter and added another 2-yard TD run in the fourth.
The Badgers had struggled the previous two times they played a Football Championship Subdivision opponent, but Wofford (1-2) only managed to hang around for a quarter because of the turnovers by Clay and Brown.
Wisconsin turned it into a laugher in just under 5 minutes of the second quarter.
Leading 3-0 on Philip Welch's field goal, Wisconsin scored a touchdown on the first play of the second quarter on Tolzien's 3-yard toss to Lance Kendricks.
Borland, who also forced a fumble on a punt return in the first quarter, followed moments later with a blocked punt by slicing through Wofford's line and flipping head over heels to get his hands on Chris Tommie's kick.
The ball bounced to the back of the end zone where fellow freshman David Gilbert recovered it to make it 17-0.
On Wofford's next possession, the Terriers failed on fourth-and-4 from their own 26.
That set up third-string running back Erik Smith's 10-yard run to make it 24-0 with 10:14 left and Wisconsin took a 31-0 lead into halftime on Tolzien's 7-yard TD pass to Garrett Graham.
In Wisconsin's previous two FCS games, The Citadel scored 31 points to keep it uncomfortably close throughout in 2007 and Cal Poly scored 35 points before losing in overtime last year.
Wofford, a Spartanburg, S.C.-based school of 1,400, didn't have top running back Eric Breitenstein because of a knee injury and couldn't provide the same challenge in its first game in school history against a Big Ten opponent.
All 63 of Wofford's yards in the first half came on runs from the triple option, but the Terriers finally broke through in the third quarter.
Austin Palmer scored on a 7-yard run to capitalize on one of Wisconsin's turnovers and Palmer reached the end zone again from the 1 with 2:24 left in the game to cap scoring.