Stave attended Whitnall High School in Wisconsin and was a two-star recruit according to Rivals and Scout.com. Stave threw for 2,635 yards and 22 touchdowns as a senior. He earned 1st Team All-State honors and was the unanimous conference player of the year.
Stave redshirted at Wisconsin in 2011 and became the first freshman to start for the Badgers the next season since Jim Sorgi in 2000. His first career start came against UTEP in 2012 where he threw for 214 yards and a touchdown. He completed nine of his first 11 passes against Michigan State on October 27 before leaving the game with an injury. He would not play again until a brief appearance in the Rose Bowl against Stanford. He was named an Academic All-Big Ten selection in 2012.
Stave started all 13 games in 2013 for Wisconsin and led them to a spot in the Capital One Bowl against South Carolina. He scored his first rushing touchdown of his career against Massachusetts. Stave was an All-Big Ten Honorable Mention selection by the media and threw for 2,494 yards and 22 touchdowns and 13 interceptions. He completed nearly 62 percent of his passes in 2013 and was 9 of 13 for 80 yards and two scores in the Capital One Bowl before suffering a shoulder injury.
|2013 Regular Season||208||336||61.9||2494||7.4||22||13||65||21||1||58||16|