Real Salt Lake (15-7-6) needs one more win to clinch a fourth consecutive playoff spot.
Espindola's second goal tied Saborio for the team lead and gave Real Salt Lake a 3-0 halftime lead.
The win marked Real Salt Lake's fifth straight and moved it into a second-place tie with Seattle.
''We've demonstrated over the last two years that we can win games and go on runs,'' Real Salt Lake coach Jason Kreis said. ''We should be considered contenders for the championship. That's how we think about ourselves, for sure.''
Considering the Western Conference's third-place team came in tied with Los Angeles for the fewest goals allowed in the league (22), the early deficit was too much for the Red Bulls to overcome.
The Red Bulls (7-7-15) remained three points behind Philadelphia and Houston, who are tied at 39 points, for the conference's final playoff spot.
Real Salt Lake opened the scoring in the seventh minute when Saborio headed in his ninth goal of the season off a corner kick by midfielder Andy Williams. Saborio had position on midfielder Teemu Tainio in front of the net.
Espindola put Real up 2-0 four minutes later when defender Tim Ream mishandled a ball in the crease, allowing Saborio's front-line partner to play it off to the left of Frank Rost and knock it into a wide open net.
Espindola struck again with his ninth goal in the 21st minute, breaking between Ream and Rafa Marquez for a through ball from Collen Warner for an easy goal.
''It feels great,'' Espindola said. ''When the midfielder does a couple of touches, you see it and you gotta go.''
Warner called it a ''basic up, back, and through,'' as he knocked it back to a teammate before taking the return pass and seeing Espindola.
''He was making a run and all I had to do was put it there. We knew they'd be fighting hard, so this is good.''
Kreis wasn't surprised, as he noted that Espindola was one of the bright spots during training camp.
''He's having a breakout year,'' Kreis said.
Joel Lindpere put the Red Bulls on the board with his seventh of the season off a free kick from Rafa Marquez, who was booed throughout the night for a shaky defensive game. The Red Bulls had three other near-misses in the closing minutes as RSL crammed eight men in the box.
New York faces the Portland Timbers at home Saturday.
''I think everyone is now aware that it's a must win, it's not enough with a tie or anything,'' Red Bulls coach Hans Backe said. ''That's the consequences and the conclusion when you go out Saturday.''
