Fabian Espindola, who played for the Red Bulls last season and was selected by United in the re-entry draft, sent in a corner kick that defender Bobby Boswell flicked toward the back post, where Arnaud finished it for his first goal for D.C. The goal was the fastest for United since Chris Pontius scored in the first minute against New York on June 24, 2012, in a 3-2 loss.
After snapping a club-record 15 game winless streak last week, United (2-2-1) has won consecutive games for the first time since the end of the 2012 season.
The Red Bulls (0-2-4) had their string of four consecutive draws broken with the loss. New York, last season's Supporters' Shield winner, also was winless after six games in 2005 (0-1-5).
Boswell nearly scored himself in the 52nd minute after he headed down Espindola's free kick, but goalkeeper Luis Robles was able to deflect the shot into the air before bringing it down while standing on the goal line. Robles finished with four saves.
Thierry Henry, who returned to the Red Bulls' lineup after a one-game absence, nearly tied it in the 36th minute, but his header went wide. Henry also was in good position to tie it in the 55th minute, but his header went over the crossbar and the outstretched hands of goalkeeper Andrew Dykstra. Henry had a game-high eight shots, two of which were on frame.
New York continued to press in the second half, and Peguy Luyindula's shot from just inside the box struck the right goal post in the 73rd minute.
Australian international Tim Cahill did not travel for the Red Bulls and missed his second consecutive game with a hamstring ailment.
United backup goalie Dykstra recorded his second consecutive shutout in place of the injured Bill Hamid. Dykstra finished with four saves.