The Stars produced three goals on their first four shots of the game and drove Nashville goaltender Pekka Rinne from the contest.
Nashville cut the lead to 4-3 when David Legwand scored on the power play 4:38 into the third period, but Jamie Benn boosted the Dallas lead 30 seconds later and Michael Ryder added an empty-net goal with 2:07 to play.
Dallas won for the fifth time in seven games. Nashville lost for just the second time in eight contests.
Lindback stopped 20-of-22 shots after replacing Rinne. Nashville's comeback bid fell short 24 hours after the Predators had rallied from a three-goal deficit to defeat Columbus 6-5.
Notable deaths of 2014 [PHOTOS]