United (6-13-4, 22 points) managed only two shots on target themselves in the contest. But the performance marked D.C.'s first defensive clean sheet in 14 games, and their first in three games under new manager Wayne Rooney.
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The Eastern Conference's last-place team had conceded 34 goals in its last 12 games. That's more goals than 16 MLS teams had conceded over the entire season entering this weekend.
The Red Bulls (10-7-7, 37 points) also snapped their own defensive rough patch by posting their first defensive shutout in six MLS matches.
New York had conceded five goals in each of its two previous defeats, a 5-4 home league loss to the Colorado Rapids on Tuesday night and a 5-1 loss at Orlando City in the U.S. Open Cup semifinals the week before.
The Red Bulls finished the season series with a win and a draw in league play and another victory at D.C. in earlier Open Cup action.
Overall, the Red Bulls outshot D.C. 13-4, but saw seven of those attempts blocked by D.C. defenders.
On one of the rare times a D.C. defender wasn't present, Cameron Harper fired one-time chance high of the top left corner later in the opening 45 minutes.
In the second, New York's Patryk Klimala got free down the right flank but fired a good look on goal wide of the target in the 63rd minute.
D.C. leading scorer Taxi Fountas's header 10 minutes later didn't have nearly enough pace to beat visiting goalkeeper Carlos Coronel.