New England (6-4-7, 25 points) moved to within one point of fifth-place NYCFC and finished the season series at 1-1-1. NYCFC (8-8-2, 26 points) remained four points in back of fourth-place Orlando City, who it visits Wednesday.
Bunbury scored his fifth goal and first since getting two on Sept. 6 in New England's 2-1 win at Chicago.
The veteran midfielder scored after his teammates capitalized on some sloppiness by NYCFC.
Revs defender DeJuan Jones started the play on the other end of the field by breaking up a New York pass through the box and kicked the ball to Nguyen at midfield. Nguyen quickly passed to Bunbury, who sped past defenders Alexander Callens and Maxim Chanot before lifting a soft shot by goalkeeper Sean Johnson
Nguyen added what turned out to be the game-winner by converting a penalty kick in the 80th minute. It was his first goal of the season and first since Sept. 1, 2018 when he played for Los Angeles FC.
Callens scored on a header in the third minute of stoppage time in the second half for NYCFC.
Matt Turner tallied seven saves and nearly posted his seventh shutout of the season and 17th of his career. He withstood a late flurry in the final minutes of the first half and then made a lunging stop against Castellanos during stoppage time before being out of position for Callens' header.
NYCFC saw a three-game winning streak stopped and fell to 7-2-2 in its last 11 games. NYCFC lost despite holding possession for nearly 67 percent of the match in its second game at Yankee Stadium after playing home games at Red Bull Arena in Harrison, N.J., due to coronavirus protocols.
Johnson stopped three shots for New York.