MADISON, Wis. — Wisconsin quarterback Colton Joseph delivered through the air and on the ground Saturday, accounting for four touchdowns in the Badgers’ 31-3 win over Michigan State at Camp Randall Stadium. Joseph threw three touchdown passes and added a 47-yard rushing score. He completed 9 of 20 passes for 145 yards and ran 10 times for a season-best 130 yards, becoming the first Wisconsin quarterback to rush for at least 100 yards in a game since Tanner McEvoy ran for 158 against Bowling Green in 2014. The Badgers (4-1, 2-0 Big Ten) have won four straight, their longest such streak in five years. Tight end Jacob Harris caught a 20-yard touchdown pass from Joseph on Wisconsin’s opening drive, which covered 75 yards over 15 plays and consumed 8 minutes, 16 seconds. Wisconsin converted all four third downs on the possession. Harris and Joseph had connected for a 72-yard touchdown in the closing minutes of Wisconsin’s 24-20 comeback victory at Penn State the previous week. Harris said the team needed to build on that result rather than treat it as a destination. “As great of a win as last week was, it does you no good if you don’t continue to build on it,” Harris said. “We have to be able to stack weeks and get better every week no matter what the result is.” Wisconsin went into halftime ahead 17-3 after Gavin Lahm made a 30-yard field goal with 3:56 remaining in the second quarter. Michigan State’s Liam Boyd answered with a 31-yard field goal with nine seconds left in the half. Joseph’s 47-yard run made it 24-3 with 10:36 left in the third quarter. Malachi Coleman’s 46-yard reception for a touchdown, with 7:56 remaining, closed the scoring. Coach Luke Fickell said he had urged Joseph to be more aggressive as a runner. “Two weeks ago I challenged him: ‘Run to win. Run to score,’” Fickell said. “And I think we saw a little bit more of that today.” Michigan State (2-3, 0-2) lost its third straight game. The Spartans struggled to sustain drives, converting 5 of 18 third-down attempts and 1 of 6 fourth-down tries. Starting quarterback Alessio Milivojevic completed 15 of 32 passes for 103 yards. Jaziun Patterson led the team with 62 rushing yards on 18 carries. Michigan State coach Pat Fitzgerald said the offense did not execute consistently, citing missed opportunities across the line and at receiver. Wisconsin was penalized six times for 67 yards, but the Spartans did not turn those flags into enough offense. The Badgers next visit No. 23 UCLA on Oct. 17. Michigan State is scheduled to host Illinois next Saturday.