Trained by Charlie Appleby and only ridden by Kirby after he lost the ride on John Leeper to Frankie Dettori, the Godolphin-owned son of Frankel shot clear in the final furlong to give his handler a second win after Masar in 2018.
Richard Hannon's Mojo Star, a 50-1 chance, ran a huge race to be four and a half lengths away in second, with the winner's stablemate Hurricane Lane, winner of York's Dante Stakes, another three and a quarter lengths back in third.
Yorkshire challenger Gear Up set the early gallop, with Kirby on his heels aboard Adayar and Youth Spirit also prominent in the early stages.
Favourite Bolshoi Ballet was also towards the head of the field, settled in fourth on the outside, while the well-fancied John Leeper was restrained in last place by Frankie Dettori until the field reached Tattenham Corner.
Gear Up started to drop away with two furlongs to run, allowing Kirby a run up the inside rail and he soon put daylight between himself and the field. It was a race-winning move.
Mojo Star finished well from off the pace to take second, with Hurricane Lane also keeping on at the one pace for minor honours, but Adayar prevailed by four and a half lengths.
Bolshoi Ballet and John Leeper were both ultimately well beaten and the result provided Kirby with a happy ending, after he was jocked off John Leeper earlier in the week in favour of Dettori.
Oisin Murphy was booked for Adayar, but Kirby then replaced him on Thursday.
Yet a measure of racing's respect for Kirby, who broke Adayar in at his pre-training yard, is that Murphy was amongst the first to congratulate him.
Kirby, who is nearly six feet tall, struggles with his weight each day and joked that he had been going to Epsom for three average rides.
Kirby said: "There's been ups and downs, it's racing, but when it comes to Charlie Appleby, he's a top man. I can't thank him enough. He's a real gentleman and a great trainer."
Of the favourites, Bolshoi Ballet did not stay and faded into seventh while Gear Up was 10th of the 11 runners.