The Edmonton skip scored four in the seventh end in Draw 5 against Saskatoon's Laycock to take an 8-5 lead and eventually improve to 3-0.
Martin is coming off a loss in the final of the first Grand Slam event earlier this month to Glenn Howard of Coldwater, Ont.
Winnipeg's Jeff Stoughton and Calgary's Kevin Koe are also perfect through the early matches.
Stoughton finished the day with an 8-4 win against Winnipeg's William Lyburn, while Koe scored once in an extra end to edge Winnipeg's Mike McEwen 6-5.
Meanwhile, Switzerland's Peter de Cruz beat Brad Gushue of St. John's, N.L., 8-5 and Rob Fowler of Brandon, Man., defeated Edmonton's Brendan Bottcher 5-3.