Connauton, a native of Edmonton, was taken by the Vancouver Canucks in the third round (No. 83) in the 2009 NHL Draft after his freshman season at Western Michigan. He had been eligible to be drafted in 2008 but wasn't selected.
After being drafted in 2009, Connauton opted to play with the Vancouver Giants of the Western Hockey League and had a breakout season with 72 points (24 goals, 48 assists) in 69 games. He signed with the Canucks on April 28, 2010, and spent most of the next three seasons with Vancouver's affiliates in the American Hockey League before being traded to the Dallas Stars on April 2, 2013.