The win for the Calgary-based rink comes a year after they had to settle for silver at last year's event.
Park and Thomas will now represent Canada at the world championship from April 18-25 in Sochi, Russia.
"Anytime you have a chance to represent Canada on the world stage there is an immense sense of pride," said Thomas after the game. "We just hope we can play our best and bring home a medal."
Both players have previous international experience. Thomas is one of just two skips to win back-to-back gold medals at the world junior men's championship— winning in 2006 and 2007. This year's Brier winner John Morris also accomplished the feat in 1998 and 1999. Park won a silver medal as the alternate for Kaitlyn Lawes team that represented Canada at the 2009 world juniors.
Park and Thomas finished round robin play with a 6-1 record and beat Ontario's Lynn Kreviazuk and David Mathers in the semifinal earlier in the day.
The pair will be bidding to become just the second Canadian team to ever reach the podium at the world mixed doubles championship since the event's inception in 2008. Alli Flaxey and Sean Grassie won a bronze medal in 2009 at Cortina d'Ampezzo, Italy.