The B.C. skip took advantage of an ill-timed miss from Quebec's Sarah Dumais in the 10th end and scored four points in an 10-8 victory Wednesday.
With the win, Brown's team from Kamloops improved its overall record to 6-1. The records from the preliminary round carry over to the championship round-robin.
"(Quebec) deserved to win that one," Brown said. "We didn't. The way we played, it was totally their game, but we came out on top. We just weren't getting our shots in the right spots, ever. We were really fortunate."
But she says no team wins a Canadian championship without a few lucky victories.
"We have to take it for what it is," Brown said. "We just have to be sharper next game and win it outright, we can't rely on luck. We have to rely more on skill now."
Quebec dropped to 2-5 with the loss.
In other women's championship round games, it was: Manitoba 8 Yukon 7; Ontario 9 New Brunswick 8; and Saskatchewan 11 Nova Scotia 3.
In men's action, Alberta's Thomas Scoffin improved to 6-1 with a 10-4 win over New Brunswick's Josh Barry.
"Step one is complete, we made the championship round, and that was a battle of a game," Scoffin said. "It was a lot closer than the score indicated."
In other championship-round men's play, it was: Ontario 6 Quebec 4; Nova Scotia 9 Saskatchewan 4; and Manitoba 8 B.C. 7 in an extra end.
The top three teams after the championship round robins conclude on Friday will qualify for the playoffs. The first-place teams will move onto the final, while the second- and third-place teams will meet in the semifinals.
The six teams in each gender that didn't qualify for the championship round are playing a seeding round robin to determine final rankings for next year's tournament in Liverpool, N.S.
In women's seeding-pool play, Newfoundland and Labrador edged P.E.I. 7-6, while in men's play the Yukon downed the Northwest Territories 14-2 and Northern Ontario defeated P.E.I. 8-5.