Selected by the Ottawa Senators in the seventh round (No. 204) of the 2011 NHL Draft, Dzingel played three seasons at Ohio State University. As a junior in 2013-14, he led the Big Ten Conference in goals (22) and points (46) and was a finalist for the Hobey Baker Award, given to the top player in NCAA Division I.
In 2016-17, his first full NHL season, Dzingel scored 32 points (14 goals, 18 assists) in 81 games, then contributed three points (two goals, one assist) in 15 Stanley Cup Playoff games. His goal with 5:19 remaining in the third period of Game 7 in the Eastern Conference Final against the Pittsburgh Penguins forced overtime, but the Penguins won 3-2 to advance to the Stanley Cup Final.