Winner of the Yorkshire Cup, Ascot Gold Cup and Goodwood Cup, the top-class stayer, owned by Bjorn Nielsen, landed the bonus for connections with a performance that was full of guts and determination.
It may not have been straightforward for the 4-11 favourite, but the John Gosden-trained four-year-old ultimately got the upper hand in the final furlong to beat his old rival Count Octave in the hands of Frankie Dettori.
Petitioner, wearing the Nielsen second colours, set a sensible gallop until the turn for home, where Count Octave took over.
Stradivarius took some time to find his feet, but he knuckled down to his task and once he hit the front at the furlong pole, he kept up the gallop to beat Count Octave by a length and half.
Aidan O'Brien's Idaho was four and a half lengths away in third place.
Gosden said: "Full marks to the owner, he's been trying to breed a Derby winner for years and he ends up with a Cup horse!
"But seriously, he's passionate about breeding and puts a lot of time and effort into it, so he deserves it.
"It's an extraordinary achievement. The horse has a lot of determination, but also a lot of class.
"I wouldn't say he was at his sparkling best today, Rab (Havlin, on Petitioner) did a good job setting a pace and it was a good job he was there otherwise there wouldn't have been much pace at all.
"I think he's better off a really strong pace. But we can't complain as we won.
"Just briefly Frankie had his ground taken. He hates coming up the rail at York, he won right down the middle on Mark Johnston's horse yesterday and was determined to do the same, but he ended up on the rail."
Reflecting on the year, he said: "The highlight was definitely Ascot, that was a terrific race, we never knew if he'd stay or not.
"After the first leg we were only thinking of Ascot, after that then it (bonus) became a real possibility, then of course, after Goodwood we were only ever going to be thinking of it.
"When it was announced we thought it was a great incentive, but would be very hard to do, so I'm thrilled to do it in the first year."
Of a potential crack at the Prix de l'Arc de Triomphe, Gosden said: "It looks very hot this year, so we'll just have to see."
Dettori was in flying dismount form, but felt his mount was not at his very best.
He said: "I didn't feel the horse was as good today as at Ascot, only his courage and class got him through.
"I'm usually worried sometimes he can take a hold, but today he was very quiet, he didn't carry me with his usual enthusiasm.
"He's had a hard season, being in every two-mile championship race from the start of the season can take its toll, but his class and courage saw him through.
"Show me the money!"
A proud Nielsen said: "To win just one leg of the incentive is huge, they are all prestigious races.
"To win four, first of all you need a tremendous horse, but you also need an enormous amount of luck and a very talented trainer to bring the horse to a peak four times in a season.
"As for next season, it seems pretty obvious to keep him to the same races. I've no inclination to take him to Australia (Melbourne Cup), it is very hard for a horse to come back from there and show the same form."
Anna Lisa Balding, wife of trainer Andrew, said of the gallant runner-up: "He ran a fantastic race and hopefully that might get his rating up a bit and get him to Australia (Melbourne Cup).
"Oisin (Murphy) has given him a lovely ride and the horse behaved so well today as well. Sometimes he's a little bit on it.
"We're absolutely delighted. We'll get him home and make the trainer make the decisions, but that (Melbourne Cup) would be the plan."
She added: "It was a helluva run and luckily we didn't ruin the party!
O'Brien said of Idaho: "He ran a very good race. We're delighted really."