Dreisbach played college football at the University of Michigan and is best remembered for his performance in his first game as a Wolverine, the 1995 Pigskin Classic against Virginia. In Lloyd Carr's debut as Michigan head coach, the Wolverines trailed 17–0 at home in the fourth quarter before the redshirt freshman Dreisbach engineered three scoring drives, the last culminating with a touchdown pass to Mercury Hayes as time expired for an 18–17 Michigan victory. Dreisbach set Michigan records for pass attempts (52) and passing yards (372) in the game; both marks have since been broken.
Dreisbach was saddled with injuries later in the 1995 season and was replaced by Brian Griese. Dreisbach served as Michigan's starting quarterback the first eleven games of 1996, but did not start in the bowl game due to injury. Dreisbach saw limited action as a backup to Griese in 1997 due to injuries in the pre-season. Dreisbach was expected to start his senior season in 1998, but lost his starting job to redshirt junior Tom Brady.
Dreisbach drew interest from professional scouts despite not starting a game during his junior and senior seasons, and was signed as an undrafted free agent. Between 1999 and 2003, Dreisbach spent time on the rosters of three NFL teams, the Oakland Raiders, the Buffalo Bills, and the Detroit Lions, but never saw any regular season action. Dreisbach played in NFL Europe for the Scottish Claymores in 2002 and from 2003 to 2008, he played in the Arena Football League. Dreisbach is currently retired from playing football and coaches in Austin, Texas at Austin High School.