Epping scored deuces in the second and fifth ends and added singles in the fourth and seventh for the victory at Mattamy Athletic Centre.
Edmonton's Brendan Bottcher topped Brad Gushue of St. John's N.L., 6-4 in the other quarter-final match.
Epping will play Winnipeg's Mike McEwen in Sunday morning's semifinal while Bottcher will take on Olympic champion Brad Jacobs of Sault Ste. Marie, Ont.
Earlier Saturday, Scotland's Eve Muirhead defeated Edmonton's Heather Nedohin 8-4 in quarter-final play.
Muirhead scored three in the final end for the victory. She will meet Ottawa's Rachel Homan in the semi.
Russia's Anna Sidorova also reached the semifinals at the final Grand Slam of Curling event of the season with a 6-3 win over world champion Alina Paetz of Switzerland. Sidorova takes on Edmonton's Val Sweeting on Sunday.
The women's final is scheduled for Sunday afternoon while the men will play in the evening.