The team took nine of a possible 12 points at the Ryder Cup-style curling competition Friday to grab a 13-8 lead on the World squad in the overall points race through two days.
The first team to 30.5 points will claim the WFG Financial Cup.
The North Americans, who lost to the World team in last year's event, capped their day by winning two men's team games on Friday night and tying another.
"Boy, what a day," said Edmonton skip Kevin Martin after his team rolled to a 6-3 win over Sweden's Niklas Edin. "Everybody's been playing really, really well. We've got the momentum, and hopefully we can keep it going, but it's a long way to the finish line yet."
Martin's rink took control with two points in the first end and scored three in the fourth to cruise home with the victory on the centre sheet, where he was able to watch the two other North American men's teams playing on either side of him.
"It takes a lot of pressure off of you, and it adds so much pressure to the other team that we're playing with the scoreboards the way they were," Martin said. "That all sort of feeds on itself in this event. So far, so good."
In other action, U.S. champion Heath McCormick picked up his first win of the week, taking advantage of a short-handed World squad skipped by Norway's Thomas Ulsrud for an 8-3 win. Ulsrud lost second Christoffer Svae early in the game with a stomach issue that also was affecting players on Tom Brewster's Scottish team.
"It was nice to get that one," said McCormick, who rebounded after a disappointing 8-7 loss to Edin on Thursday. "We felt like we let one slide last night. We were pretty much in control and I missed a couple bad shots. So to come out and play well again felt nice. It's nice that we can be part of this team and contribute to this team.
"We feel like we belong."
Brewster's rink salvaged half a point from the evening when he drew for a deuce in the eighth end to pull out a 5-5 tie with Glenn Howard of Coldwater, Ont.
"Every point, every half point makes a difference," said Brewster. "It's about reaching that 30.5 points and we're half a point closer to reaching that. It was hard fought tonight but it was good. We're seeing a couple of the others guys (on the World team) go down and it's not great. We've just got to dig deep and scrap for everything."
There will be six more traditional team games (three men's and three women's), each worth one point for a win, and one-half point for a tie. All games are eight ends and there are no extra ends. For the six mixed doubles and six singles matches, one point will also be awarded for each victory, one-half point if tied.
The six skins games (two mixed, two women's and two men's) on Sunday will offer a total of five points per game, with the first six ends of each game worth one-half point each, while the seventh and eighth ends are worth one point each. In skins, a count of at least two with last rock or a steal is required in order to win an end. Otherwise, the points carry over.
The winning side receives $52,000 ($2,000 per member, including captain and coach), while the losing side gets $26,000 ($1,000 per member, including captain and coach). As well, the side that generates the highest point total in Sunday's six skins games will receive an additional $13,000.
Each team has won four Continental Cups.