Canada improved to 5-2 with the win, tied for second place in the standings with Norway, Russia, and Sweden and within reach leader Kyle Smith of Scotland (5-1).
In women's action Canada's Corryn Brown also beat her continental rival, rebounding from a 4-3 loss to Switzerland with a 10-4 rout over the U.S.
"It's a pride thing," Dunstone said. "It was good to see Canada come out on top of these North American battles."
After American skip Korey Dropkin stole a point in the first end, Dunstone's Winnipeg rink responded with a deuce in the third and took a 5-2 lead after five ends.
"We had a really strong fifth end and I think we made eight straight shots there," Dunstone said. "After that we kind of took the momentum from them. We only had control after we got that deuce in nine. A two-point lead is nothing on the quality of teams here. I felt most comfortable once we got that four-point lead in the last end."
Brown's rink from Kamloops, B.C., came up just short against Switzerland's Michelle Gribi (2-4). Trailing 4-2 in the 10th, Brown attempted a double to lie two and force the extra end, but just missed, taking only one for the 4-3 loss.
Brown and her team rebounded against American skip Miranda Solem, stealing two ends on the way to a 10-4 win.
"We definitely played a little more aggressive, put a little more rocks in play, and watched how things ended up," said Brown, who now sits at 2-5 and will not make the playoffs. "We have nothing to lose, to be honest. So we might has well give it everything we've got."
Scotland's Hannah Fleming remains the only unbeaten women's team (7-0) with Japan's Sayaka Yoshimura (5-2), Russia's Alina Kovaleva (4-3) and Denmark's Stephanie Risdal Nielsen and (4-3) in the mix.
Brown has the day off Wednesday, while Dunstone's rink faces Norway.