The sophomore forward scored at 8:40 of overtime when he took a shot on a two-on-one breakaway.
"I never shoot, but this time I decided to shoot," said Marcoux. "I just shot it as hard as I could."
The goal capped a thrilling rally by the OUA silver medallists, who rebounded from three three-goal deficits in the game.
"We did not start the way we wanted to, but we showed a lot of character," UQTR head coach Marc-Etienne Hubert said. "We have faced a lot of adversity. This team has believed in each other all year."
Guillaume Asselin scored twice for UQTR while Martin Lefebvre, Felix Plouffe and Billy Lacasse added singles.
Chris Owens, Remy Giftopoulos, Boston Leier, Taylor Makin and Mike Cazzola scored for the Axemen.
The Patriotes will face Alberta in Saturday's semifinals after the Golden Bears toppled the StFX X-Men 5-1 in the other quarter-final.
Kruise Reddick, Jordan Hickmott, T.J. Foster, Travis Toomey and Brennan Yadlowski supplied the offence for Alberta while Kurtis Mucha made 12 saves for the win.
Blake Gal scored for the X-Men. Drew Owsley stopped 29 shots in a losing cause.