The Timbers skipped away to a two-goal lead after Bright Dike and Darlington Nagbe both struck by the 32nd-minute mark but the Red Bulls managed to level the score by half-time at the Red Bull Arena.
First, Jan Gunnar Solli sat up a tasty cross for Kenny Cooper to head home against his old club in the 43rd minute before ex-Everton star Cahill scored in controversial circumstances two minutes later. The Australian teed up a shot for Dax McCarty whose effort struck Timbers defender David Horst with a whistle blown straight away for possible handball but the ball fell for Cahill who struck home a left-footed volley amidst the confusion.
The goal was left to stand giving him his opening strike in MLS before the Red Bulls completed their fight from behind when Heath Pearce nodded home another Solli cross in the 82nd minute to secure all three points.
The victory enabled New York to remain second on the Eastern Conference table, two points behind Sporting Kansas City, whilst the unlucky Timbers dropped to the bottom of the West.