Cotter took a 3-2 lead in the third end, but Koe scored three in the fifth to take hold of the match.
Koe then added a point in the sixth for a 6-3 advantage. Cotter scored two in the seventh end but Koe added a point in the eighth.
“This was my seventh Grand Slam final and my first win,” said Koe, who won a world title in 2010. “It’s been a long time coming.”
Earlier, Ottawa's Rachel Homan dispatched Winnipeg's Chelsea Carey 8-3 to win the women's championship.
“We’ve been doing really well on the Slam side of the events, but it’s nice to finally win a final,” said Homan. “I think we picked the right one to win and this is just an amazing feeling.”
Homan led 3-0 after three ends, 5-3 after six and then added three points in the seventh and final end.Suggest a correction