Second-half strikes from Nathan Sturgis and Deshorn Brown were key to the win. Sturgis poked home two minutes into the second period after a scramble in the penalty area and half-time substitute Brown added a second in the 68th minute, tapping in Chris Klute's cross-shot at the far post.
The Red Bulls had the ball in the net in the 74th minute but Tim Cahill was offside. They stayed two points behind the Montreal Impact having played three games more.
Robbie Keane scored two penalties in the last five minutes to give the Los Angeles Galaxy a 2-1 win over the Columbus Crew.
Bernardo Anor's looping header put the Crew ahead in the 78th minute, but Keane's 86th-minute leveller from the spot was perfectly placed and he produced a carbon copy in stoppage time to seal the points.
The day's other game, between FC Dallas and Chivas USA, finished goalless.