Goals from Brazilian forward Fabio and defender Kyle Duncan either side of half-time settled Saturday's (AEST) contest for Red Bulls, which recorded a fourth consecutive home victory.
The result inflicted Nashville's first defeat of the season, also seeing it slide down to eighth in the east as Red Bulls moved up to third, five points behind leader New England Revolution.
Fabio, who joined Red Bulls in February, netted his first goal for the club with a fine volley in the 37th minute after Patryk Klimala's crafty flick-on.
Ten minutes into the second half, Duncan added a second, collecting the ball at halfway, running forward and unleashing a low left-foot finish from outside the box.
Real Salt Lake scored twice in stoppage-time to end their three-game run of draws courtesy of a 3-1 victory over Vancouver Whitecaps.
Erik Holt and Damir Kreilach struck at the death, helping Real Salt Lake move up to fifth spot in the Western Conference.
The late double blow also condemned the Whitecaps to a fourth successive defeat.
Kreilach opened the scoring in 43rd minute after Albert Rusnak's classy pass, but Vancouver levelled 10 minutes after half-time from an unmarked Brian White at the back post.
The game appeared destined for a draw before Holt headed home from a long Aaron Herrera throw into the box in the 92nd minute, with Kreilach nodding in another to seal the win three minutes later.