The home side got off to a terrible start as RSL scored three times in just over 20 minutes with Alvaro Saborio netting the opener before two goals from Fabian Espindola in a 10-minute span.
Joel Lindpere scored in the 69th minute for New York, but it wasn't nearly enough to overcome the slow start, snapping a four-game unbeaten streak for the Red Bulls.
New York nearly took the lead in the third minute when a deflected cross from Lindpere struck the crossbar, but Salt Lake took control of the first half from there.
A corner kick from Andy Williams found Saborio 10 yards from goal as the striker shook free from his marker and nodded the ball into the upper-right corner of the net.
New York's Tim Ream then handed the visitors their second goal four minutes later when a terrible pass inside his own penalty area allowed Espindola to easily beat goalkeeper Frank Rost.
Collen Warner played provider on the third goal when he worked a one-two with Saborio and lofted a through ball over the top of the defense for Espindola, who rolled his shot past Rost and inside the left post.
Lindpere was the one player who looked dangerous for New York and he had a rocket from 30 yards tipped off the crossbar by Salt Lake goalkeeper Nick Rimando midway through the second half.
But Lindpere finally found the net in the 69th when Rafael Marquez lobbed a free kick to the penalty spot, where Lindpere scored on a brilliant scissors kick.