Rinne earned his 11th straight win with the performance, continuing a hot streak during which he has allowed two or fewer goals in 10-of-11 games since Jan. 5.
Martin Erat supplied much of Nashville's offense, notching a goal and two assists as the Predators improved to 4-0 against St. Louis this season.
Mike Fisher and Sergei Kostitsyn also found the net for the Predators, who leapfrogged the Blues for second place in the Central Division with the victory.
Chris Porter scored and Jaroslav Halak stopped 34-of-36 shots in the St. Louis loss.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys