The one-mile-six-furlong contest is the namesake of the entire meeting and Rotherham-born Swift, 25, admitted it had always been an ambition to win the big handicap.
He employed excellent waiting tactics aboard the 25-1 shot to come from the rear to claim Europe’s richest handicap by a length from the Queen’s horse Tactician, with Investissement third and Modun fourth.
“It’s great for me being a Yorkshire lad, there’s nothing better for me than to win this race,” said Swift.
“To ride in a race like this is really important and to win it is something special.
“It’s amazing and it might take a week to sink in.”
Malton-based trainer Brian Ellison wallowed in a personal triumph, also sending out the fifth-placed Saptapadi as Moyenne Cornice became the first Yorkshire-trained winner since Les Eyre’s Far Ahead in 1997.
“The plan was to hit the front late, I knew he would love the ground and I said to Dale he wouldn’t be out of the first four,” said Ellison.
“It’s fantastic. We like to target races like the Northumberland Plate, the Ebor and the November Handicap.
“I said to Dale, the first thing you do is to ride him for a place then go and win it.”
The Ebor apart, the day belonged to Frankie Dettori as the ever-popular Italian weighed in with a 199-1 treble on Parlour Games (9-1), Opinion Poll (3-1) and My Propeller (4-1).
His first two winners were for Godolphin and trainer Mahmood Al Zarooni.
Parlour Games galloped on stoutly to outstay Whiplash Willie by three-quarters of a length in the Betfred Melrose Stakes, while Opinion Poll won the Weatherbys Insurance Lonsdale Cup for the second year running as he outstayed Yorkshire Cup winner Duncan.
Al Zarooni said: “The main target for this horse is the Group Two at Ascot on Champions Day and there’s also the Doncaster Cup he could go to before that.”
Dettori completed his trio on My Propeller for soccer star owner Joey Barton and trainer Peter Chapple-Hyam in the Julia Graves Roses Stakes.
Not be outdone, six-times champion Kieren Fallon enjoyed a double on Risky Art (6-1) and York Glory (5-2 favourite) in the last two races to be crowned top jockey at the four-day meeting with four winners.
He beat Dettori, who also had four, by having two thirds to the Italian’s one.
While Ellison was savouring his moment at York, another Brian enjoyed a similarly satisfying afternoon at Sandown.
Brian Meehan was delighted to see his filly Theyskens’ Theory return to winning form in the De Vere Venues Atalanta Stakes after disappointing at Royal Ascot last time.
With many jockeys engaged at York, the Frenchman Davy Bonilla flew over to help her battle through the rain-softened ground to beat Modeyra by half a length.
Meehan said: “It was a bit about finding out whether she should continue here or go to America, where her owner is based, and that’s something we’ll talk about.
“A Group One win is the most important thing and I would say the Sun Chariot at Newmarket is well within her scope.”
It looked a very competitive renewal of the Atalanta, although the same could not be said for the Sunshine Coach Solario Stakes, a Group Three for two-year-olds won by Raven’s Pass and, most recently, Native Khan.
But it was hard to quibble with the performance of Jeremy Noseda’s Talwar (9-4), who strode five lengths clear of his three rivals after leading from start to finish under Jimmy Fortune. Paddy Power offer 33-1 for next year’s 2000 Guineas and Stan James 20-1.