Menard and third Martin Crete, second Eric Sylvain and lead Philppe Menard capitalized on Manitoba's mistakes and were more in control than the 7-6 final score might suggest.
They moved on to play Alberta's Kevin Koe in the semifinal later Saturday night to see who would play B.C. in the final Sunday.
Menard and his team may not have started well at the Tim Hortons Brier but they're finishing on a tear.
"It's true, like we're 3-4 and pretty much on the bubble, but we managed to play a bunch of good games in the row and momentum seems to be on our side," said the 38-year-old Government of Canada human resources manager.
They finished at 7-4, claiming the fourth and last playoff spot.
Saturday they looked as relaxed and confident as they have in all their recent games and continued to play aggressively.
Quebec and Manitoba traded deuces in the second and third ends but mistakes in five forced Stoughton to try a hit for a single and he rolled out for a steal.
"The fifth end was just a terrible combination of shots," said Stoughton, who at 50 said his team would review their future at the end of the season.
"I mean we came deep on Mark's draw, let 'em make a double, then Jon bumped ours out, then we missed the hit and roll, then I missed the double, then I missed the hit and stick for one."
It was the same in six when Stoughton was heavy on a draw to give up a steal of two.
"I think the sixth end was the turning point," said Menard. "When I threw my last rock it went back eight but that piece of ice was really, really fast and I guess he got caught too, so he slid through and after that we were able to control most of the game and avoid major damage."
Manitoba came back with two in seven to close within one but Menard's deuce in eight gave the 2006 Brier winner the margin he needed.
Quebec has only won the Canadian title twice. Stoughton alone has won it three times and Manitoba leads the country with 27 titles.
He gave Menard full credit for the way he has taken on the top three at this Brier and beaten them all in the round robin.
"They're just a good team but I think they get up more for some of the bigger teams than they do for the lesser teams," he said.
"They played really well against Koe yesterday morning, they were great again tonight so whatever it is, it's working."
Menard's win in the final round-robin game against Alberta left the top finishers tied at 9-2 and bumped Manitoba into the 3-4 game because of a tie-breaking formula based on draws to the button.