After the first two shooters for both teams came up empty, Nashville's Roman Josi scored when the puck trickled under the pads of Kari Lehtonen. Stars forward Vernon Fiddler slipped on his way to the net, but recovered and was able to get the puck in to extend the game.
Seguin, who had been 1 of 6 in shootout chances, scored the winner after Predators center Matt Cullen was denied.
Dallas holds the eighth and final playoff spot in the Western Conference with 89 points, two ahead of Phoenix after the Coyotes got a point for an overtime loss at Columbus. Both teams have three games left.
The Stars play twice more at home, including the makeup Wednesday night against Columbus of the March 10 game when Stars forward Rich Peverley collapsed on the bench in the first period because of an irregular heartbeat.
Jamie Benn scored his 34th goal for the Stars, who are trying to avoid another late-season collapse.
Dallas lost its 2011 regular-season finale with a playoff spot on the line, and missed the postseason again after losing its final five games in 2012 and then going 0-4-1 down the stretch last season.
Gabriel Bourque scored two goals for Nashville, which with 82 points and only three games left have no possibility of getting into the top eight.
Lehtonen had 27 saves in regulation and overtime. In the shootout, it looked as if he had stopped Josi's shot before the puck slid from under his legs and just past the line.
Pekka Rinne stopped 28 shots, and remained at 161 victories, tied for the most in Nashville franchise history.
The Stars missed a big chance in the third period when they had a two-man advantage for 1 minute, 38 seconds. They got three shots off in that span, but couldn't get one past Rinne.
The Stars were up 1-0 less than 2 1/2 minutes into the game when Alex Goligoski scored on a backhand from the top of the circle.
Nashville got even when Bourque scored his first goal early in the second period, after Craig Smith worked the puck around the back of the net and passed out to the middle for the shot.
Benn scored on a breakaway in the second period, but Bourque tied the game midway through the third period.
Notes: Ray Whitney missed his third game in a row for Dallas with a lower body injury. ... There was a brief delay with 3:16 left in the third period when arena workers had to replace one of the sheets of plexiglass that had a large star-shaped crack after a hard shot, apparently by Stars center Cody Eakin. ... Goligoski had a goal and six assists in the season series against Nashville that Dallas won 3-2.