Martin took an early lead after winning the second end and taking $4,000 with a first end carry-over.
Stoughton replied to take the third end and pulled ahead following carry-overs in the fourth and fifth ends to take $13,000 in the sixth end.
Both Stoughton and Martin made incredible shots to force a seventh end carry-over, with the eighth end also going undecided. Stoughton's shot secured the remaining $22,000 in prize money plus a $15,000 winner's bonus to bring his final tally at the two-day event to $70,500.
Stoughton beat Brad Gushue in Saturday's semifinal while Martin downed Canada's 2014 Olympic representative Brad Jacobs to advance.