Luis Silva and substitute Eddie Johnson both scored in the second half as the East high-flyers accounted for the Red Bulls in front of 19,453 spectators at the Robert F Kennedy Memorial Stadium on Sunday - a record crowd for United in 2014.
United were just a point clear of rivals Sporting Kansas City after Wednesday's mauling at the hands of the Los Angeles Galaxy, but the team's game in hand saw them edge clear.
Ben Olsen's men have collected 46 points from 26 matches in the East, while defeat for New York has left the Red Bulls languishing two points outside the final play-off spot in sixth position.
Both goalkeepers were kept busy during the opening 45 minutes but neither side could make the breakthrough.
Australia international Tim Cahill came closest to netting the opener for New York with two minutes remaining in the half after his low shot cannoned off the far post.
United finally broke the deadlock 12 minutes after the interval thanks to Silva, who pounced on a mix up between Red Bulls keeper Luis Robles and defender Ibrahim Sekagya to tuck the ball away into an empty net.
Johnson - a replacement for goalscorer Silva in the 66th minute - came off the bench to seal the points in the first minutes of injury time.
The United States international striker beat the offside trap and drove towards the penalty area before lobbing the ball over Robles.
Meanwhile, the LA Galaxy closed to within two points of the lead in the Western Conference after downing basement club Chivas USA 3-0.
Gyasi Zardes' brace and a goal from substitute Robbie Keane helped the in-form Galaxy to a resounding win over their city rivals.
A run of four consecutive wins now has the Galaxy on 46 points, two behind leaders the Seattle Sounders.
Chivas are two points adrift of the San Jose Earthquakes, though the cellar-dwellers have played an extra game.