Cahill scored the opening goal of the scintillating contest with an 11th minute header before Fabian Espindola doubled the advantage but a hat-trick from Alvaro Saborio had the league-leading RSL ahead with only minutes remaining.
A frenzied end ensued with Espindola and Dax McCarty giving the Red Bulls a thrilling comeback win over a team labelled as the best in the league by Cahill.
"I said I wanted to get as many minutes under my belt when I play in this league because you want to be fit and you always want to be competing against the best teams, the best teams, and they are one of the best, you know, I watched them yesterday for an hour after training and footballing wise they're brilliant," said the Australian midfielder.
"They're one of the most complete teams I've seen in the league. That's my first opportunity to play against them. So, you know they're a good football team, a very good football team so a lot of credit to them."
The victory allowed the Red Bulls to go within one point of Eastern Conference leaders Sporting Kansas City and they now sit just two behind overall leaders RSL.