New York (13-12-9, 48 points) clinched the seventh and final spot in the Eastern Conference. The Red Bulls edged out D.C. United by one point to clinch their 12th straight playoff berth and finished the regular season by going 7-1-4 over the final 12 games after a difficult start.
Fabio scored 35 seconds in when he got a pass from Cristian Casseres Jr. and finished off the sequence with a right-footed shot that whizzed past the right leg of Nashville goaltender Joe Willis' diving attempt.
Hany Mukhtar scored the tying goal in the 37th minute as Nashville (12-4-18, 54 points) secured the third spot and finished off an unbeaten home season (8-0-9). According to ESPN, it was the seventh time a team went unbeaten at home in MLS history.
Mukhtar got his 16th goal off a set piece. Facing soft coverage, he sliced a long shot that grazed the top of Fabio's head and deflected over the leaping try of Red Bulls goalkeeper Carlos Coronel.
Coronel made three saves and survived a frenetic final 20-plus minutes, including one sequence in the 67th minute when Nashville missed several chances to score. He stopped one Mukhtar shot and then watched Mukhtar go wide on a header.
Coronel also survived another big chance right before stoppage time. In the 89th minute, he slightly came out of the box to stop Ake Arnaud Loba's right-footed shot moments after a header by Jhonder Cadiz sailed wide.
Willis finished with four saves, including a leaping and diving stop on Casseres in the 51st minute, and then survived Omir Fernandez clanging a shot off the right post in the 88th minute. He also made a diving stop on Tom Edwards shortly before Mukhtar leveled the match.