The Predators climbed past Detroit into fourth place in the Western Conference, a spot that carries with it home-ice advantage in the opening round.
Dallas came up just short of a post-season spot for the second year in a row. The Stars had been in first place in the Pacific Division before losing five of their last six. Dallas missed the playoffs last year by two points.
Pekka Rinne recorded his fifth shutout of the season, making 28 saves.
Bouillon broke the scoreless tie 4:28 into the third and Hornqvist scored with 2 minutes to play.
With Dallas eliminated and Colorado falling to Columbus, the last of the eight Western Conference playoff teams were determined.
Los Angeles, Phoenix and San Jose all wrapped up a post-season spot, although no first-round pairing has been established.