Sissons gave Nashville a 1-0 lead at 8:06 of the first period when he received a backhand pass in the left face-off circle from Forsberg, who had intercepted a clearing attempt along the boards.
"We had a pretty productive night," Sissons said of his line. "I think we were all feeling pretty good finding each other and making plays, so hopefully we can continue to build that."
Gibson, who made 49 saves in a 3-2 shootout win against the Vegas Golden Knights on Wednesday after missing the previous five games with an undisclosed injury, stopped Nino Niederreiter at 10:19 on a 2-on-1 and saved a redirection by Mattias Ekholm at 11:32 to keep it a one-goal game.
Carrick then tied it 1-1 at 2:20 of the second period. After Justin Kirkland intercepted a breakout pass, Jayson Megna dropped the puck to Urho Vaakanainen who stepped into a slap shot that deflected off Carrick's hip.
"When we are playing our best, we are winning those puck battles, playing with the puck and making the right decisions when we get the puck," Carrick said. "We just didn't really do that tonight."
Yakov Trenin restored the Predators' lead when Ducks defenseman Cam Fowler was unable to clear the rebound on his initial shot at 9:04 to make it 2-1.
"We're doing our best to compete every night. That's the reality of where our team's at," Anaheim coach Dallas Eakins said. "When you are a team like that, you can't make any mistakes."
Forsberg extended it to 3-1 at 13:20, scoring after Terry was unable to clear the puck following shots by Sissons and Parssinen.
"I thought tonight we were hungry to get rebounds, to look to score, to screen the goalie, and that makes a big difference; being there versus being there with a purpose," Nashville coach John Hynes said. "I thought tonight we were there with a purpose."