Josi skated from behind the net into the slot, and his wrist shot hit defenseman Esa Lindell’s skate and popped over goalie Anton Khudobin.
Nashville won for the second time in six games to move within a point of Central Division leader Winnipeg.
Dallas is 1-4-1 in its past six games.
Filip Forsberg tied the game at 3 with 1:44 left in the second period, 21 seconds after the Stars took their first lead with goals 26 seconds apart by Lindell on the power play and Tyler Seguin.
Jason Spezza scored the first of three Dallas goals in the second period. It was his first in 20 games since Dec. 29. He and Lindell each had a goal and an assist.
Pekka Rinne made 36 saves in his 21st win of the season for the Predators.
Khudobin stopped 42 shots.
Boyle scored at 10:50 of the first period, seven seconds after Dallas had killed the game’s first power play. Khudobin stopped a close-range wrist shot, but Boyle skated in front to knock in the rebound.
The crowd reacted with boos for Boyle, who eight seconds before had driven Dallas scoring leader Seguin into the boards at the other end.
Boyle went into the penalty box for holding at 17:39 of the first, but the Predators killed that penalty despite five shots on Rinne.
Spezza tied the game with a wrist shot from the top of the slot at 3:31 of the second period. It was the first Dallas goal in 145:43 of playing time.
At 10:57 of the second, Grimaldi gave Nashville a 2-1 lead. He took a pass from Ryan Hartman, skated in alone on Khudobin and faked toward the left before putting the puck on his forehand and sliding it inside the right post.
NOTES: C Craig Smith (lower-body injury) was out of Nashville’s lineup for the first time since Dec. 21, 2017. … Stars G Ben Bishop sat out his sixth straight game, and LW Blake Comeau missed his third. They have upper-body injuries. … Boyle’s 15th goal was his second in seven games since the Predators traded a draft pick to New Jersey for him on Feb. 6. … Lindell’s power-play goal was the Stars’ first in 13 man advantages over six games. … The season series ended with Nashville 3-2 and Dallas 2-1-2.
Predators: Host Los Angeles on Thursday to begin a three-game homestand.
Stars: Play Vegas on Thursday in the second of a four-game homestand.