Formerly trained in Germany, but now with French master Andre Fabre, the four-year-old held the challenges of Irish raiders Ace and Azamour to take the spoils.
As early leader Shake The Bank faltered, Christophe Soumillon assumed control but kept his head and refrained from asking Shirocco for his maximum effort until within the final two furlongs.
Snatching a decisive advantage off the home turn, the winner who paid 8-1 on the American tote stayed on stoutly down the home straight to beat the staying-on Ace and Kiren Fallon by one and three-quarter lengths.
Azamour, who had been well down the field in the early stages, finished strongly to take third just ahead of last year's Arc winner Bago.
Shirocco, who only recently joined Fabre from German trainer Peter Schiergen, was giving Soumillion his first Breeders' Cup success.
The rider said: "We knew the number one horse (Shake The Bank) would make the pace and we didn't want to go too fast.
"But if he gets behind he doesn't like it. He likes a fast pace and soft ground and he got both today. This is just a dream.
"To win in New York is unbelievable."
Fabre added: "He acts on any ground as he showed when he ran very well in the Arc when the ground was faster but he is a strong galloper and the very fast pace helped him.
"He will stay in training next season and go for all the big international events over a mile and a half."
Fallon said: "The blinkers helped he should have been wearing them all along but the ground certainly didn't.
"He is a top-of-the ground horse and this deep track was not to his advantage. I suppose he could come back next year and have another try."
Azamour's disappointed trainer John Oxx added: "Mick (Kinane) reported he lost his place three and a half furlongs out and if not for that, he would have won.
"It cost him valuable momentum and though he stayed on, the winner had flown. The ground didn't help either. That is his last race and I will miss him. He lacked some of his zip today but he is a tough horse who never lets you down and he ran his heart out."
Ouija Board was denied back-to-back victories at the meeting when Bobby Frankel sent out the longest-priced winner of the Filly & Mare Turf as Intercontinental was returned at over 15-1 on the local Tote.
Having missed the break, Ouija Board had to be niggled along by Jerry Bailey to get into mid-division down the back straight.
But despite making progress around the home turn, the Ed Dunlop-trained filly never quite looked as if she was going to be able to reel in the winner and went under by a length and a quarter.
However, Dunlop refused to be disappointed at Ouija Board's defeat.
"She ran a great race but the winner was better drawn and had much more speed than us off a soft lead," he said.
"Our filly wants a mile and a half now but she ran a phenomenal race considering that she was nearly retired at the beginning of the season. I am very proud of her."
A trip to Hong Kong or Japan may now beckon for Ouija Board, having proved that she is over her midsummer injury troubles.
Of the other European raiders, Favourable Terms finished fifth, Karen's Caper 10th and Mona Lisa 11th, while Godolphin's Sundrop was all but pulled up at the back of the field.
Whipper fared best of the European team when flashing home in fourth in the Mile.
It was Artie Schiller and Garrett Gomez who denied hot favourite Leroidesanimaux to take the spoils, with Gorella third.
Jeremy Noseda's runner Majors Cast ran well to finish fifth but the well-fancied Valixir beat only one rival home.
Noseda said: "He ran a huge race he just came to the end of his tether on that ground."
And Whipper's trainer Robert Collet commented: "Unfortunately my horse got stopped and it is such a shame because that was his last race."
Bailey signed off from what may well have been his last Breeders' Cup when taking the biggest race of the night, the $4.68m Classic aboard 9-4 favourite Saint Liam.
Australian hope Starcraft looked a danger to all when looming up behind the leaders around the final bend, but Luca Cumani's charge faded once brought wide into the straight.
Aidan O'Brien's Oratorio also ran disappointingly and finished well in rear.
"Knowing it was a mile and a quarter today rather than a mile I didn't expect the same kind of explosion as he has shown before but I always felt confident that I had everything in my sights," said the veteran Bailey.
"I am going to take a break after Thanksgiving to spend some time with my family and we will talk about my future then."
Having performed consistently all year, Saint Liam is to be retired to stud at the end of the year, while Starcraft will remain in America.
Cumani said: "He didn't find anything in the straight. I can't really blame the draw because the winner started from next to us, so perhaps it was the distance.
"The owner (Paul Makin) is keen to keep him over here to run him in the Cigar Mile at Aqueduct."
Folklore provided the peerless D Wayne Lukas with his 18th training success at the Breeders' Cup when landing the opening Juvenile Fillies' under Edgar Prado.
Stevie Wonderboy came fast and late to deny front-runner Henny Hughes and take the Breeders' Cup Juvenile and complete a double for Gomez.
Lost In The Fog's status as the banker of the meeting after 10 consecutive wins was blown apart as Silver Train and Prado also completing a double got the better of a dramatic photo finish with the Gomez-ridden Taste Of Paradise in the Sprint.