Stanzi took over as starter at Iowa as a sophomore beginning in the 2008 season. He completed 150 passes for 1,956 yards with 14 TDs.

On November 7, 2009, during his junior season, Stanzi was replaced by James Vandenberg after suffering a sprained right ankle. It was later confirmed that Stanzi had surgery on his ankle. Stanzi returned at the conclusion of the season to lead Iowa to an Orange Bowl victory over Georgia Tech. Stanzi ended up passing for 2,417 yards and 17 touchdowns in his junior season – completing 56.2 percent of his attempts.

Stanzi was 14–4 in his career as Iowa’s starter going into his senior season, and in July 2010, Stanzi was named to the 2010 Davey O’Brien National Quarterback Award and Manning Award watch lists. He was also a finalist for The 2010 Premier Player of College Football Trophy which is awarded based on fan votes.

Stanzi returned to Iowa in 2010 with 9 touchdowns and no interceptions through his first four games. He completed 19-of-25 passes with three passing touchdowns on September 24, 2010.

One of Stanzi’s most memorable moments of the 2010 season occurred on November 6 in a game against Indiana, in which he connected with Marvin McNutt for a 52-yard touchdown which put Iowa up 18–13 with 2:56 remaining in the game. Stanzi put up big numbers in the 2010 season with a 167.2 quarterback rating along with 22 touchdowns. Stanzi ranked third in the nation in passing efficiency.

Stanzi graduated from Iowa in December 2010 with a B.A. in interdepartmental studies from the College of Liberal Arts and Sciences.

Stanzi was selected with the 135th pick in the 2011 NFL Draft by the Kansas City Chiefs. Stanzi was activated for the first time in his NFL career for the Chiefs against the New England Patriots on November 21, 2011. At the end of the 2011 NFL season, Stanzi was second-string behind Kyle Orton.

Stanzi was expected to be the backup to Matt Cassel, and competed in the 2012 preseason with Brady Quinn, who was signed by the Chiefs on March 17, 2012. However, Quinn eventually won the number two spot.

Stanzi was released by the Chiefs on August 25, 2013.

The Jacksonville Jaguars claimed Stanzi off waivers on August 27, 2013. He was released on September 28 and re-signed on September 30. The Jaguars released Stanzi on August 29, 2014.

The Houston Texans signed Stanzi to their practice squad on December 16, 2014. The New York Giants signed Stanzi off the Texans practice squad to a Reserve/Future contract on January 8, 2015. On September 5, 2015, he was waived by the Giants. The Detroit Lions signed Stanzi to their practice squad on September 8, 2015. Stanzi participated in rookie minicamp on a tryout basis with the Cleveland Browns in 2016. However, he went unsigned, and spent 2016 out of football. In April 2017, Stanzi participated in The Spring League, a developmental football league intended to provide a platform for free agents to be seen by scouts.

On July 29, 2017 against the Hamilton Tiger-Cats, Stanzi made his professional regular season debut when he entered during garbage time of Calgary’s 60–1 victory. Stanzi’s first CFL pass attempt was a completion to receiver Anthony Parker. Stanzi finished the game with one completion on two attempts, for 5 yards. Stanzi finished the year with 4 completions on 8 attempts for 53 yards, no touchdowns, and 2 interceptions, all of his playing time coming during garbage time. The Stampeders advanced to the 105th Grey Cup, but were defeated by the Toronto Argonauts. Stanzi’s opposing quarterback during the Spring League, McLeod Bethel-Thompson, who likewise spent 2017 as a CFL backup, was a member of the victorious Argonauts roster. The Stampeders would win the Grey Cup the following year, but Stanzi missed out, having been released after the first game of the 2018 regular season.