Visiting Vancouver mounted a second-half comeback with Kenny Miller scoring the winner late.
Early in the second half, the Red Bulls took the lead thanks to an own goal from Greg Klazura, who made his MLS debut in the match. Thierry Henry fed Jonny Steele down the left. Steele attempted to pull the ball back in the box, and it took a sharp deflection off Klazura to beat his goalkeeper near post.
Vancouver has conceded eight of its 17 goals in the first 15 minutes of the second half.
Klazura went off with an injury shortly after to cap a tough debut. Lee Young-Pyo replaced him, making an immediate difference. The South Korean crossed from the right flank, and Eric Alexander failed to clear properly. Jordan Harvey smashed a volley into the ceiling of the net to equalize.
In the 75th minute, Jamison Olave tripped Kenny Miller to pick up his second yellow of the match and earn an ejection.
Miller again affected the match in the final 10 minutes. The Scot beat Kosuke Kimura to a Russell Teibert cross and headed under Luis Robles for the winner.
The loss marked New York's first in eight games. Vancouver won away for the first time since July 4.