The visitors’ quick start was rewarded when McCarty headed home Sacha Kljestan’s corner after just three minutes.
Wright-Phillips headed home to double the lead before he spectacularly put the Red Bulls three-up with an acrobatic volley.
McCarty lost his marker shortly after the break to head home his second of the game before Alex Muyl powerfully drove home a fifth shortly after.
Gonzalo Veron and Gideon Baah completed the annihilation late on as the Red Bulls emerged victorious in the Hudson River derby once again.
Early goal for visitors sets them on their way
Patrick Viera’s side were unbeaten in their last five games going into the game with their rivals, but it was a start to forget as they were behind in the opening exchanges.
Kljestan swinging corner found the head of an unmarked McCarty, who powerfully found the back of the net.
Just four minutes later, their lead was almost doubled when Lloyd Sam came close with an effort after McCarty laid the ball off for the midfielder.
City didn’t manage to create their first opening until 20 minutes, and even then it came to nothing as a last ditch challenge stopped any chance of an equaliser.
The Red Bulls continued their dominant display and after McCarty’s header was well saved from Josh Saunders, they did finally manage to get a crucial second goal in the game.
Wright-Phillips nets twice in five minutes
Mike Grella twisted and turned the defence inside-out, and his dinked cross was headed down past Saunders by Wright-Phillips.
Half-time was approaching, and still the hosts offered very little, but Grella linked with Wright-Phillips once more to round off an emphatic first 45 minutes.
Grella’s cross was headed up by Aurelien Collin before Wright-Phillips produced a spectacular overhead kick to send the ball sailing past a helpless Saunders, and into the bottom corner.
The visitors began the second-half just as they finished the first-half, and they didn’t look like easing up the pressure on their opponents.
Wright-Phillips, whose second goal was his 50th in MLS, drilled a shot from the edge of the box straight at Saunders, who could only push the effort over the bar.
Five-up 11 minutes after half-time
The resulting corner was swung in by Kljestan and McCarty lost Ronaldo Matarrita, who was more interested in pulling his shirt, and headed past the keeper for his second of the game.
It was five minutes later when the Red Bulls broke with frightening pace, and Muyl, who had only been on the pitch for two minutes, smashed home Wright-Phillips’ pull-back.
City had a chance on 70 minutes when Andrea Pirlo’s shot was deflected to David Villa, but his afternoon was summed up when he shot straight at the keeper from two-yards out.
Pirlo’s curling free-kick had the home fans on one side of the ground believing the hosts had a goal back, but it could only find the side netting before the Italian was replaced by Frank Lampard.
Rout completed with two further goals late on
The visitors continued to hunt in packs and wanted more goals after several chances went begging, they finally managed to find a deserved sixth in the game.
Felipe’s swinging delivery, from a free-kick which was cheaply given away, was headed home at the back post by substitute Veron from two-yards out.
Sam had another chance two minutes later, which went astray, but the Red Bulls found their seventh on 89 minutes when substitute Baah prodded home from close range.
It really was a day to savour for the Red Bulls and their travelling supports, they managed to inflict the heaviest defeat on City in their franchise history.