Brandon Hagel and Corey Perry scored, and Jonas Johansson made 29 saves for the Lightning (46-21-6), who are 6-0-2 in their past eight games.
Tampa Bay moved into a tie with the Buffalo Sabres, who each have 98 points, for the top seed in the Atlantic Division, with the Lightning having played one fewer game.
Filip Forsberg had a goal and an assist, and Justus Annunen made 25 saves for the Predators (34-31-9), who have lost three straight and remain one point ahead of the Los Angeles Kings for the second wild-card spot out of the Western Conference.
Joakim Kemell scored his first NHL goal to give Nashville a 1-0 lead at 8:31 of the second period. Kemell was pushed from behind by Lightning defenseman Erik Cernak when he had the puck, with both going into the net. The goal call was confirmed as good after a review.
Guentzel tied it at 1-1 at 13:32 after Darren Raddysh sent a shot to the net that Gage Goncalves tried to redirect. The puck instead ended up on Guentzel's stick in the low slot, where he punched it past Annunen.
Hagel gave Tampa Bay a 2-1 lead at 4:33 of the third period, taking a backhand pass from Guentzel and snapping a shot from the slot past Annunen to the far post.
Just 20 seconds later, Forsberg restored the tie game 2-2 at 4:53. After Fedor Svechkov sent the puck to the net from just inside the blue line, it deflected off Forsberg first and then off the skate of Charle-Edouard D'Astous to get past Johansson.
Perry put the Lightning ahead for the 3-2 final at 6:52. Emil Lilleberg tried to get the puck to Guentzel for a redirection, and the puck got through Annunen's pads and Perry stuffed it past the line from the doorstep.
