Stoughton has won three in a row heading into the playoffs. He lost his opening round-robin match to Regina's Steve Laycock.
Martin tried to score a deuce in the fourth with Stoughton leading 2-1, but after a measurement his rink was only able to claim a single to tie it.
Martin went ahead 3-2 after Stoughton couldn't drag his final shot to the button, giving up a steal of one in the fifth. The teams then traded singles heading into the eighth.
Martin (2-2) now faces defending Players' champion John Epping (2-2) in a tiebreaker.
In other Draw 13 action, Glenn Howard scored a triple in the seventh end to pull ahead and win 5-3 over Winnipeg's Mike McEwen.
The Coldwater, Ont., rink finished the round-robin with a 4-0 record.
McEwen qualified for the playoff round with a 3-1 record.
Canadian champion Brad Jacobs and his Team Easy Express squad were victorious in extra ends with a 5-4 win over Calgary's Kevin Koe.
Jacobs, from Sault Ste. Marie, Ont., finished with a 3-1 record and advanced to the playoffs.
Koe (2-2) will face Brad Gushue (2-2) of St. John's, N.L., in a tiebreaker match.