Ottawa rebounded from a 4-0 loss at Carolina on Friday night.
''Sometimes you're a little tired mentally on the back-to-back and you got to reset, but that's why there's three periods,'' Senators forward Mathieu Joseph said. ''I thought we had a good talk in the third, we showed up and the boys delivered.''
Watson broke a tie at 4:31 with a deflection of Travis Hamonic's point shot and Batherson fired a wrist shot from the slot past past goalie Sam Montembeault at 5:18.
Julien Gauthier added his first goal for the Senators with 8:03 to go. Gauthier came over from the New York Rangers a week ago along with a seventh-round pick for forward Tyler Motte.
Derick Brassard and Shane Pinto also scored for Ottawa and Mads Sogaard made 29 saves and had his first career assist.
''He was great,'' Senators coach D.J. Smith said about Sogaard. ''We shouldn't have given him that many opportunities, but in saying that, that's why you have a goalie. And clearly, he's calm and he's doing his thing.''
Mike Matheson and Nick Suzuki scored for Montreal.
''I liked our game but I didn't like the result,'' Canadiens coach Martin St. Louis said. ''It just kind of got away from us in the third. Not so much structurally, just missed assignments. First two periods, I thought we were outplaying them so obviously it wasn't a 5-2 game.''
Brassard opened the scoring for Ottawa with 4:48 left in the first period, tipping Nick Holden's long wrist shot past Montembeault.
Just 58 seconds after Michael Pezzetta fought Watson, Matheson tied it for Montreal at 4:29 of the second. Matheson beat Sogaard off his own rebound.
Suzuki gave Montreal the lead on a breakaway at 8:46 of the second with his 20th goal of the season. Pinto tied it at 2 with 6:09 left in the third, deflecting Alex DeBrincat's centering pass from the corner past Montembeault.
Senators: Host Detroit on Monday and Tuesday nights.
Canadiens: At San Jose on Tuesday night.
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