Born in Ibbenbüren, North Rhine-Westphalia, Unnerstall finished his development at FC Schalke 04 after joining at the age of 18. In April 2010, after featuring regularly for the B-team, he signed a professional contract until 2012. For the 2011–12 season, coach Ralf Rangnick announced Unnerstall as second-choice behind Ralf Fährmann. His professional debut took place on 31 July2011, in a 11–1 away win against FC Teningen for the first round of the DFB-Pokal; in October, he agreed to an extension until June 2013. On 15 October 2011, after Fährmann's ejection early in the game, Unnerstall made his Bundesliga debut, in an eventual 1–2 home defeat to 1. FC Kaiserslautern. After it was revealed the former had suffered a serious cruciate ligament injury he became the starter, remaining as such even after the signing of veteran Timo Hildebrand and earning praise from manager Huub Stevens. Before the 2012–13 campaign started, Unnerstall agreed to a new deal until 2015. He continued to battle with Hildebrand for starting duties, and was also first-choice during the team's run in the UEFA Champions League; he also committed several mistakes in home matches, which led to fan criticism. During the 2013 off-season, Unnerstall was linked a move away from the club. Nothing came of it, however, and he remained as third-choice behind Fährmann and Hildebrand. On 24 January 2014, Unnerstall was loaned to Swiss Super League side FC Aarau. His first match took place eight days later, in a 1–1 draw against FC St. Gallen; he was later chosen Player of the Month for this display.
On 21 May 2014, Unnerstall joined Fortuna Düsseldorf as a replacement for Fabian Giefer, for a reported fee of €250,000. He spent most of his tenure as backup to Michael Rensing, featuring rarely in the 2. Bundesliga and adding two appearances in the 2015–16 edition of the domestic cup. Increasingly frustrated with his lack of playing time, and occasionally demoted to the reserves, Unnerstall was also afflicted with pneumonia in early 2017.
In June 2017, Unnerstall signed for VVV-Venlo on a two-year deal for an undisclosed fee. On 18 May of the following year he agreed to a three-year contract at fellow Eredivisie team PSV Eindhoven, being immediately loaned to his previous club.
