The victory eliminates the Dallas Stars from playoff contention.
The Predators have now made the playoffs in seven straight campaigns, tying them with the Washington Capitals for the second-longest active streak.
The club owned an 11-16-1 record on March 15, but the team turned its season around with a 19-7-1 stretch since.
Nashville will open the postseason against the top-seeded Hurricanes. It will be the first playoff meeting between the two clubs.