Brian Wright's second-half goal at Yankee Stadium proved to be the winner for the Revolution, who boosted their playoff chances with the win while handing NYCFC its first home loss of the season.
The loss extended City's winless run to four matches.
For the Revolution, the win was their first victory since June and moved the club to within three points of the sixth-placed of the Montreal Impact in the Eastern Conference.
Wright had already struck the post before scoring his first MLS goal in the 71st minute for Brad Friedel's men.
Cristian Penilla's effort was parried by City goalkeeper Sean Johnson and Wright reacted quickest to tuck away the rebound for the match-winner.
While NYCFC's form has been poor of late, the club remains in solid playoff position, sitting third in the table and 15 points clear of the playoff-chasing Revolution.