The Predators won their ninth straight playoff game in Nashville going back to last postseason.
Nashville will play either Anaheim or Edmonton.
The Predators and Blues were tied through the first 40 minutes for a third straight game and fourth overall in this series when Johansen skated up the slot for a pass from Viktor Arvidsson and beat Jake Allen with a backhand.
Allen kept the Blues close as he had all series, stopping Filip Forsberg on a breakaway with 13:31 left. But Jarnkrok scored with a minute to go to clinch it, amping up Nashville's celebration.
The Predators got forward Craig Smith back for the first time in this series after he was hurt in Game 3 against Chicago in the first round. And the Blues got back left wing
Nashville had Grammy winners Lady Antebellum sing the national anthem, and forward Kevin Fiala, who broke his left leg in Game 1, wave the towel to rev up the fans who were ready for the puck to drop.
The Predators weren't.
St. Louis took the first seven shots and went up 1-0 on Stastny's goal, a wrister just 2:04 into the game off assists from
Tarasenko's shot from the right circle hit off Rinne, then Stastny who knocked the puck in for the goal. The Blues even took the first two penalties of the game, and Nashville couldn't take advantage of the man advantage with sloppy puck-handling and too many turnovers.
It was the first even-strength goal the Predators had allowed in the first period this postseason.
The Predators needed only 35 seconds into the second to tie it up.
Johansen, Arvidsson and Filip Forsberg came into this game having combined for only three points in this series after getting 15 in sweeping Chicago.