Martin, a former world and Olympic champion from Edmonton, defeated Gushue of St. John's, N.L., in seven ends.
Colwater, Ont., native Glenn Howard, the reigning world champion, lost his opening round-robin match, 6-5 to Toronto's John Epping in extra ends.
Eighteen of some of the best men's curling teams in the world are squaring off at the event for a share of a $100,000 purse.
Kevin Koe, also from Edmonton, beat Norway's Thomas Ulsrud 6-5 in extra ends.
Howard trails Koe on points in the Grand Slam series. Koe won the first event of the season, the Masters, and also placed second to Howard in the Skins, earning $38,500.
Winnipeg's Jeff Stoughton lost his first match 5-2 to Brad Jacobs' rink, while Sweden's Niklas Edin edged Sven Michel of Switzerland 6-5 with two in the eight end.