The Galileo filly had beaten dual 1000 Guineas winner Winter twice already this campaign, but was racing over a mile and a half for the first time.
Ryan Moore made a bid for home early, obviously in no doubt about her ability to stay the distance, but the favourite Bateel cruised up alongside her. When asked to go and win the race, though, Bateel simply could not get past Hydrangea and in the final 100 yards the 4/1 shot began to pull away again.
Hydrangea eventually won by two lengths, with Coronet back in third.
On equalling the record, O'Brien said: "It's incredible for everyone, they all put in so much hard work, day in day out. We're a small link in a big chain and I'm delighted for everyone - it's a magic, special day. The chain is so long and we're so glad to be a little link in it."
He added of the winner: "She's by Galileo and they will not stop, their will to win is incredible. She pulled out more and it was Ryan's idea to run her as he thought there was a chance she'd get the trip. We weren't sure, but she did."
Moore said: "What Aidan O'Brien has done this year is remarkable and it is a massive team effort. Everyone who looks after these horses, they put in so much time.
"The filly has been on the go all year and has got better and better. I thought she had a good chance, I just hoped the ground would be a bit better than it was.
"I'm delighted for Aidan."
Trainer Francis-Henri Graffard said of Bateel: "Fantastic. There are no excuses today.
"My filly did everything, she tried really hard, she came with a lot of petrol under her and she came upsides Hydrangea.
"When Ryan really asked his filly she ran away from me. I was very very upset, but looking at the replay there were no excuses and I'm really proud of her."
Graffard added: "She did a fantastic job for us this year and we have to discuss with the owners about next year. She has earned her place at stud and she'll definitely be going for a break now.
"I would be happy to keep her and breed her, but every ending would be happy
"I think she was at her top in the Vermeille and she was at her top today. She is a competitive Group One filly
"She's a great filly, I don't think I could have done more with her, she was spot on for today, had her conditions and was beaten by a better filly on the day."
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