Dvorak started his playing career with the Chicago Mission U16 and U18 teams. After his impressive seasons in Chicago he was chosen sixth overall in the USHL Futures Draft, and in the 8th Round of the 2012 OHL Draft. He played the 2012–13 season with the Chicago Steel in the United States Hockey League, but the following year decided to move to Canada to play for the London Knights of the OHL. After the 2013–14 season, he was drafted in the second round of the NHL Entry Draft by the Arizona Coyotes, who also drafted his former and current teammates Max Domi and Brendan Burke. His rise to stardom began in the 2014–15 season, where he was second on the team with a staggering 109 points, only behind prodigy Mitch Marner. On April 18, 2015, Dvorak signed his first professional contract, agreeing to a three-year, entry-level deal with the Arizona Coyotes. He was assigned on an amateur try-out contract to make his professional debut with AHL affiliate, the Portland Pirates. Dvorak was named co-captain of the Knights at the beginning of the 2015–16 season, sharing the honor with Marner. Throughout the season, Dvorak played on the top line alongside teammates Marner and Matthew Tkachuk. At the season's end, he led the team with 121 points, surpassing his previous score. Dvorak helped the London Knights win the 2016 Memorial Cupchampionship game at the ENMAX Centrium in Red Deer, Alberta to end his junior career.
Professional
On November 3, 2016, Dvorak scored his first NHL goal on goalie Pekka Rinne to help clinch a win over the Nashville Predators. Dvorak also chipped in an assist on a goal scored by Anthony Duclair to tie the game. It was the first multi-point game of Dvorak's NHL career. On October 30, 2017, Dvorak scored his first goal of the 2017–18 season to help the Coyotes defeat the Philadelphia Flyers and avoid setting a new NHL record with a 12th-straight loss to start the season. On August 9, 2018, Dvorak signed a six-year contract extension with the Coyotes. Dvorak began the 2018–19 season sidelined due to a pectoral muscle injury. On October 19, it was announced Dvorak underwent surgery to repair the torn pectoral muscle and was expected to take months to recover.
