Nick Bonino had a goal and an assist, Colton Sissons and Roman Josi each had two assists, and Pekka Rinne made 17 saves for Nashville (17-6-1), which has won four of its past five games and is tied with the Tampa Bay Lightning for first place in the NHL with 35 points.
"For as long as I've been here, we've done a good job of bouncing back after we've played games we didn't like," Watson said. "Tonight was no different. That's a good hockey team over there. They're always spirited, hard battles. We stuck to our game plan, we got on the attack and we were able to start our little homestand here off with a good win."
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Adam Henrique and Ondrej Kase scored, and John Gibson made 28 saves for Anaheim (10-10-5), which has scored two goals or fewer in six of its past eight games.
"To me, it's about defense," Ducks coach Randy Carlyle said. "We can be criticized for lack of offense, but the reality is, we need to be able to hold the opposition to one goal or two goals. That's the reality of it. Where we're set up, the way we are with our group right now and the personnel that we have in place, we have to win the 1-0 game or the 2-1 game. Simple as that."
Watson gave the Predators a 1-0 lead at 11:04 of the first period, getting the rebound off Bonino's initial shot in the crease and scoring at the left post.