Patric Hornqvist scored the decisive goal with 6:04 left in the contest and Carter Hutton stopped 14-of-16 shots he faced in the Nashville goal.
Roman Josi and Matt Cullen also scored while the Predators enjoyed a man advantage, snapping a three-game losing streak they had been saddled with in the run-up to the Olympics break.
Martin St. Louis scored a pair of goals in the first period for Tampa Bay, one of them on a power play, to take an early 2-0 lead. Ben Bishop made 26 saves.
The Lightning had nine shots on goal but only four in the second period and three in the third.