Stoughton and Lawton each scored in the 10th end to secure a spot at next year's Olympic qualifying tournament.
"It's been a tough grind this week. I'm really proud of the guys, and I think it's going to hit us in the next week that we finally did it, and we don't have to worry about anything at all for the rest of the year," Stoughton said of his Winnipeg rink. "Of course we want to go back to the Brier, but I think it will be a little less stressful."
Lawton — whose Saskatoon rink included Marliese Kasner, Sherri Singler and Sherry Anderson — won 6-4 over a Jennifer Jones team that was being skipped by Kaitlyn Lawes.
Stoughton, meanwhile, was joined by Jon Mead, Reid Carruthers and Mark Nichols in taking out Howard's foursome from Coldwater, Ont.
"We had our chances," said Howard, whose rink included of Craig Savill, Brent Laing and Wayne Middaugh. "Mark had two great tick shots in ten, and that makes it tough for us. But it was a good game, and I'm proud of the boys."
The men's and women's champions receive one of the six automatic qualification spots for the Roar of the Rings next December in Winnipeg — the tournament that will determine Canada's entries at the 2014 Winter Games in Sochi, Russia.
"It's huge," Lawton said clinching a spot. "You count points all year — the last couple of years — to get that berth. We don't have to worry about counting points, and where you're ranking ... For sure, that feels really good."
Lawes, meanwhile, is handling skip duties for Jones' Winnipeg rink after she gave birth to a baby girl two weeks ago and is also recovering from knee surgery.
Lawes' team includes Dawn Askin, Jill Officer and Kirsten Wall.
"It was an interesting year for us," Lawes said. "Definitely learned a lot and we had a wonderful time playing with Kirsten. It would have been nice to finish it off with her, but we're happy with our week at the Canada Cup. To make the final is really satisfying."