Grant made it 4-3 at 10:13 when he scored on a rebound off the end boards, but Duchene scored his second power-play goal at 11:23 to make it 5-3.
Duchene has 34 goals this season, one behind Forsberg for the Predators lead. It was his 11th goal during a 10-game point streak.
''We've gone back and forth,'' Duchene said. ''The great thing is we're pushing each other, and it's not like we're not passing to each other. If you're going to achieve greatness, you might as well do it together.''
Forsberg scored an empty-net goal with 2:03 remaining for the 6-3 final.
The Ducks entered with the seventh-best penalty kill in the NHL (82.9 percent).
"Our penalty kill has been very, very good this year; it's won us a lot of games too," Anaheim coach Dallas Eakins said. "They were able to make some really good plays, so our PK had an off night, but on a lot of nights, they've been excellent."
NOTES:David Rittich made one save for Nashville in the third period while Saros briefly dealt with a skate issue. … Forsberg matched his NHL career high for points in a game; he also had two goals and three assists in a 6-5 overtime victory against the Florida Panthers on Feb. 4, 2021. … Forsberg's previous NHL career high in goals was 33, set in 2015-16 (82 games). ... Josi has five straight multipoint games (three goals, 12 assists). ... Johansen has scored 11 points (four goals, seven assists) in his past 11 games. ... Nashville defenseman Mark Borowiecki returned after missing eight games because of a lower-body injury. He had three blocked shots, three hits and 11 penalty minutes in 13:57 of ice time. ... Jeremy Lauzon made his Predators debut after the defenseman was acquired in a trade with the Seattle Kraken on Sunday. He had four hits and two blocked shots in 18:12. ... Forward Trevor Zegras had two assists to give him 30 this season, tying defenseman Cam Fowler for the most assists by a rookie in Ducks history. ... Gerry Mayhew made his Anaheim debut on its top forward line with Max Comtois and Adam Henrique. Mayhew, who was claimed off waivers from the Philadelphia Flyers on Sunday, had one shot on goal in 13:49.