Brace, who leads his club in points with 10, including five goals, snapped a 3-3 just 11 seconds into the third period with what stood up to be the game winner.
Alex Galchenyuk had a goal and an assist for the Sting (1-3-1), who lost for the fourth time in their first five games, and Charlie Sarault and Nick Latta scored a goal apiece.
JP Anderson stopped 26 shots in a losing effort.
The Sting finished the game on a 6-on-4 power play but were unable to get the game-tying goal.
Both teams struggled on the power play as Owen Sound was 0-for-2, while the Sting scored once on seven opportunities with the man advantage.