Alex Goligoski and Brendan Morrow scored for Dallas.
Fisher gave the Predators a 3-2 lead at 9:57 of the second period. Ryan Suter's shot was blocked by goalie Kari Lehtonen. Fisher backhanded the rebound from the space between the left circle and the crease to beat Lehtonen to his stick side. Legwand closed out the scoring with an empty-netter.
Goligoski opened the scoring on a power play at 8:49 of the first. Loui Eriksson passed the puck from the left circle to Goligoski, who took a wrist shot from low in the right circle that beat Pekka Rinne.
Legwand answered with 5:34 left in the period. Martin Erat skated from behind the net and attempted a backhanded shot. Lehtonen blocked the attempt, but Legwand scored off the rebound.
The Predators took a 2-1 lead in the second period. Fisher took a slap shot from the far edge of the right circle that beat Lehtonen to the far side of the net at 2:33.
Morrow responded for the Stars with a wrist shot from behind the net that went over the top of the goal and bounced off of Rinne's head and into the net at 4:07.
NOTES: Fisher, who joined the Predators on Feb. 12, tripled his goal production for Nashville with his two goals. His only other goal with the Predators was Feb. 17 against Vancouver. ... Mike Ribeiro had two assists for Dallas. ... Legwand extended his points streak to six games.