Joe Willis finished with six saves for Nashville SC (9-2-11, 38 points), who improved to 8-0-6 at home this season. The Music City representatives also moved past Orlando City into sole possession of second place in the Eastern Conference, although the Lions host the Columbus Crew on Saturday.
NYCFC's Valentin Castellanos ended the shutout bid in the 90th minute by scoring his team-leading 11th goal and sixth in his past five matches. Sean Johnson made five saves for NYCFC (10-7-4, 34 points), who entered the match having recorded at least a point in seven of their previous eight matches (5-1-2).
Mukhtar recorded his second goal of the contest and team-leading 10th of the season in the 68th minute. C.J. Sapong played the ball ahead to Mukhtar, who tucked the ball inside the far post to give him three goals and four assists in his past five matches.
McCarty and NYCFC's Maxi Moralez each received a red card for violent conduct in the 45th minute. The players were tangled up near the sideline before Moralez pushed McCarty, resulting in players from both teams converging to the area.
The teams played with 10 men the rest of the way.