Both rinks traded singles until Martin tied the game in the eighth end, but Edin scored a single in the ninth to win 4-3.
Edin is tied with Martin and Norway's Thomas Ulsrud at 1-1 in Pool A.
Elsewhere, Glenn Howard of Coldwater, Ont., improved to 2-0 with a 4-2 victory over Toronto's Greg Balsdon (0-2).
Toronto's John Epping, who upset Howard in last year's TPC men's final in Summerside, P.E.I., is still searching for his first victory. Epping was blown out 8-2 by Jim Cotter of Kelowna, B.C., to fall to 0-2. Cotter improved to 1-1.
In women's play, national champion Rachel Homan and world champion Eve Muirhead of Scotland earned a pair of wins.
Homan's Ottawa rink scored three in the sixth end to defeat Renee Sonnenberg of Grande Prairie, Alta., 6-3. The win improved Homan to 2-0, while Sonnenberg dropped to 0-2.
Muirhead scored a point in each of the last four ends to down Calgary's Shannon Kleibrink 6-4. It was Muirhead's first win of the tournament at 1-1. Kleibrink is winless through two matches.