MADISON, Wis. (AP) — After last year's gut-wrenching last-second loss at Michigan State, Wisconsin had a surefire plan to avoid a similar fate Saturday: build a lead too big to evaporate.

The plan worked — barely.

Behind career days from quarterback Scott Tolzien and tight end Garrett Graham, the Badgers built a 21-point fourth-quarter lead and held on for a 38-30 victory in a Big Ten opener.

Tolzien threw for 243 yards and a career-high four touchdowns — three to Graham — for Wisconsin (4-0, 1-0 Big Ten), which won its third game of the season by eight points or less.

"The thing I like about Scotty is he is just constantly moving forward," Wisconsin coach Bret Bielema said. "They were taking away certain things and we thought we could take advantage of the air and he went out there and kept executing, made great decisions."

The Badgers took a 38-17 lead on Graham's third touchdown, a 23-yard catch with more than 12 minutes left in the fourth quarter.

Backup Spartans quarterback Keith Nichol and wide receiver Keshawn Martin made it interesting, hooking up twice for touchdowns in the final minutes. Martin scored on a 15-yard catch-and-run with 2:07 to go — a touchdown that was granted after a booth review — and hauled in a 91-yard scoring pass with 15 seconds left to make it 38-30. But Michigan State's onside kick attempt was unsuccessful.

"We made it a little more difficult there at the end," said Bielema, whose team wasted an 11-point fourth-quarter lead in a 25-24 loss last year. "We had a busted coverage that resulted in a big play that got us in that little tense situation in the last 15 seconds."

The Spartans (1-3, 0-1) turned the ball over four times after committing only two turnovers in three non-conference games. Wisconsin converted three of the turnovers, including two first-half interceptions, into touchdowns.

Michigan State's defense had its own struggles, as the Badgers converted 11 of 18 third-down chances.

"You can't win a football game if you can't get off the field on third down on a consistent basis," Spartans coach Mark Dantonio said. "And you can't turn it over four times."

Both offenses sputtered early, but the Badgers got on track after the first of their three interceptions. Graham made a leaping grab on a 15-yard pass in the end zone with 1:22 left in the first quarter and gave Wisconsin the lead for good with a 6-yard TD catch after Michigan State tied it at 7.

Graham's three scores tied a Wisconsin record for touchdowns by a tight end, and the senior set a new program mark for career TDs (13) at the position.

"I feel we have a comfort together," Graham said of his chemistry with Tolzien, a first-year starter. "We did a great job in the red zone, especially Scott putting the ball right in there."

Badgers running back John Clay, who lost his starting spot after fumbling three times last week against Wofford, rushed for 142 yards and a score. He bulled his way in from a yard out to cap a 12-play, 69-yard drive that was aided by three Michigan State penalties. It began when Wisconsin defensive back Chris Maragos picked off Nichol, who had just entered the game.

After the teams traded field goals to start the second half, Kirk Cousins hit B.J. Cunningham for a 20-yard scoring pass late in the third quarter to pull the Spartans within 24-17.

But the Badgers wrested the momentum back immediately, as David Gilreath returned the kickoff 32 yards and Tolzien found Isaac Anderson on a sideline route for 45 yards on the first play of the drive. Three plays later, Tolzien hit a streaking Nick Toon for a 19-yard score on the first snap of the fourth quarter.

Michigan State fumbled on its next possession at the Spartans 32-yard line, and the Badgers capitalized when Tolzien found a wide-open Graham for a 38-17 lead. The three-score margin turned out to be just enough.

"We made some mistakes down the stretch but nothing that wasn't correctable," Maragos said. "We made the big plays when we had to."

Cousins and Nichol combined for 396 yards and four touchdowns through the air. Martin had four catches for 139 yards.