Pekka Rinne made 28 saves for the Predators, who have won six in a row and sit sixth in the Western Conference with 92 points.
Alex Goligoski and Brenden Morrow lit the lamp for the Stars, who have dropped three straight. Kari Lehtonen made 28 saves in defeat.
Dallas sits two points behind Chicago for the eighth and final playoff spot in the West.
Goligoski’s power-play goal put the Stars on the board at the 8:49 mark of the first period.
Nashville tied the game with 5:34 remaining. Martin Erat controlled the puck behind the net and attempted a wrap around. A rebound was left in front for Legwand, who put the puck into the back of the net.
Fisher’s one-timer from the right circle made it a 2-1 game at the 2:33 mark of the second.
Dallas tied the game again less than two minutes later. Morrow gathered the disc behind the net and attempted to pass the puck in front. Instead, the disc deflected off a Nashville player and took a weird bounce before sneaking past Rinne.
Fisher gave the Predators the lead for good at the midway mark of the middle stanza. Ryan Suter fired a shot on net from the point. Fisher stopped the puck in front and put a backhander past Lehtonen.
The Stars had a golden chance to tie the contest late in the third period. Suter was sent to the box for hooking with two minutes left. Dallas then pulled Lehtonen for two extra skaters.
But Legwand scored on the empty net with 3.6 seconds remaining to seal the victory.
Nashville and Dallas split four meetings this season…The Predators have won five straight on home ice and are sporting a 22-8-7 record as the host this year…The Stars started a five-game road trip on Saturday.