A goal from Dave van den Bergh in the 28th minute was enough for New York to reach their first MLS Cup final.
"I think we have to congratulate the guys, and the post," New York coach Juan Carlos Osorio said. "I have been disappointed sometimes with our luck, but I think we got it today."
Real Salt Lake hit the post three times on the frustrating night for the team playing in front of a sellout crowd of 20,008 at Rio Tinto Stadium.
"Tonight it was just one of those nights with chance after chance," Real Salt Lake coach Jason Kreis said. "I don't know what else you can do. I drove myself to laughter on the bench. It was either that or cry."
New York, one of the original teams that started with MLS in 1996, also benefited from goalkeeper Danny Cepero's seven saves.
"This is great, but now we have a chance to really go for the biggest trophy in the United States," Osorio said.
Cepero added: "For us the most important thing is our mentality. Everybody's equal in the playoffs and in this league any team can beat any other team on any night."