Blake spent three years playing college soccer at UConn, before signing a Generation Adidas contract with Major League Soccer. He registered 37 shutouts over his three years in goal for the Huskies, winning the Big East Goalkeeper of the Year Award in 2011 and 2012 and the AAC Goalkeeper of the Year Award in 2013. He was named a semifinalist for the Hermann Trophy in 2013.

Blake was selected by Philadelphia Union first overall in the 2014 MLS SuperDraft. Originally anticipated to be the Union’s starting goalkeeper, he was deputized to the bench when the Union signed designated player, Raïs M’Bolhi. Blake would make his first appearance for the Union in a friendly match against Crystal Palace in July 2014. He would make his first competitive start for the Union in a 1-0 win against Montreal Impact who debuted Didier Drogba as their new designated player. Blake would start for five of the remaining eight matches in the 2015 season. One of his most notable performances was on 26 September 2015, playing against New England Revolution, where Blake set a Union team record for saves in a match with 10 stops to preserve a 1-1 draw.

Blake made his debut Jamaica national football team start on 2 March 2014, versus Barbados, a 2–0 win. Blake earned his first medal for Jamaica later that year, winning the 2014 Caribbean Cup and earning the Golden Gloves award in the process.

During the 2016 season, Blake cemented himself as the clear starting goalkeeper for the Union. In July 2016, he was included in the roster for the 2016 MLS All-Star Game. He was also selected to the 2019 MLS All-Star Game as the Union’s only representative.