The Senators killed two penalties before starting their first power play at 15:25 of the first period. Tkachuk scored in the low slot off a touch pass from Batherson to give Ottawa a 1-0 lead at 16:24.
"Great play by Drake," Tkachuk said. "Just tried to get a whack on it. From then on, it just felt like we played a really solid game, a really mature game, and just followed the game plan to a T."
Brassard finished on the rush to make it 2-0 at 18:19.
"We took three penalties in the first period, which you can't do, but Talbot was good wire to wire," Ottawa coach D.J. Smith said. "It's unfortunate the shutout is not his. He certainly deserved it."