Brossoit made 38 saves in his season debut for the Jets (2-1-0), who lost 3-1 at the Toronto Maple Leafs on Monday.
"The first half of this game, Ottawa came out really, really strong," Brossoit said. "It seemed like they wanted to take advantage of the fact we had two games in two nights. So we weathered the storm, and once that happened, we started to push, and we have enough veterans and enough skill that it always feels like we have a chance."
Josh Norris scored his first NHL goal, and Murray made 24 saves for the Senators (1-1-1).
"Other than not taking care of the puck in the third period and overtime, we had good energy, we had good [offensive] zone time," Smith said. "We did a lot of good things tonight."