Ryan O’Reilly and Ryan Ufko also scored for the Predators (31-28-9), who have won consecutive games. Justus Annunen made 25 saves.
Predators goaltender Juuse Saros missed the game because of an upper-body injury and is day to day.
Frederick Gaudreau scored, and Joey Daccord made 24 saves for the Kraken (31-28-9), who have lost two in a row and six of eight.
Ufko gave the Predators a 1-0 lead at 6:14 of the first period, scoring on a one-timer from the point off a pass from Brady Skjei.
Gaudreau tied it 1-1 at 18:40 when he redirected a Chandler Stephenson pass in the slot.
O’Reilly then gave the Predators a 2-1 lead on the power play at 7:11 of the second period. Steven Stamkos took a shot that was deflected by Forsberg, and O’Reilly got to the rebound and beat Daccord from the edge of the crease.
Forsberg scored into an empty net make it 3-1 at 18:10 of the third period.
Kraken forward Ryan Winterton did not play because of an illness.