The Fugue struck a blow for the fillies with an emphatic victory in the Red Mills Irish Champion Stakes at Leopardstown.
John Gosden's charge shrugged off concerns about the ground when outpointing her rivals.
The six-strong field came down the centre of the track in the straight as William Buick made his challenge to the leader, Trading Leather.
Al Kazeem tried to haul back Lord Lloyd-Webber's four-year-old but to no avail as The Fugue (4-1) prevailed by a length and a quarter. Trading Leather, who made most of the running, was third.
There was disappointment as the Aidan O'Brien-trained Kingsbarns was eased off by Joseph O'Brien in his belated first race of the season.
O'Brien had withdrawn his other declared runner, Declaration Of War, because of the rain-softened going.
Afterwards a relieved William Buick said: "I was worried about the ground, but it worked out well.
"She's one of the greats now. She's been so unlucky and should have won so many times last year. I'm just glad she's getting the rub of the green.
"She's always been special and has always been a special one for in the yard everybody. She's very good and has arguably beaten the best around at the moment.
Winning owner Lady Lloyd Webber said: "I'm totally speechless. I was thinking the ground wasn't right and I nearly didn't get on the plane.
"John (Gosden) kept saying it was good ground, but I think the ground went slightly away from her. It was a worry, but she is so versatile.
"It's amazing. After Dar Re Mei I thought we'd have to wait 20 years for another star, then The Fugue came along. We breed our own horses and race our fillies.
"This is the third generation and it's just unbelievably exciting to have a world class filly of this quality.
"I didn't really expect to reverse the Al Kazeem form. He has beaten us twice but she was ill in the Eclipse and now you look at that, maybe she should have won it so the form is absolutely spot on.
"We'll have to head to the west (for the Breeders' Cup). At least it won't rain like this."
"She's beaten the colts in a championship race and it was a great performance the way she did it."
John Gosden admitted he had been concerned by the state of the ground but was pleased he decided to run.
He said: "We walked the track twice before racing and I'm glad we decided to run now.
"There's a sense of relief. The ground yesterday would have been perfect but luckily the heavy rain has only really started now.
"If we'd got that three hours before racing, we wouldn't be standing here now.
"After coming over, I wasn't inclined to go back to England and then cross the Channel for the Prix Vermeille next week."
The Fugue was winning her first Group One in mixed company and Gosden believes the form is truly out of the top drawer.
"It was a proper race. The first three went a solid gallop - Kevin (Manning on Trading Leather) didn't mess around. It was a proper, even test and she came through well," he said.
"I'm really thrilled. There's some good solid form lines there with Trading Leather and Al Kazeem.
"The ground was just on the easy side of good, it was never soft.
"I said to William to just go inside the final furlong, he went a bit before that but I think he did the right thing because you don't want to leave it too late and end up looking stupid."
Gosden will now consider the options for his star filly, with another trip to the Breeders' Cup meeting, where she finished an unlucky third last year, a possibility.
"Sometimes you get fast ground for the Arc. When Sea The Stars won it was good ground but last year it was bottomless when we tried to run in the Prix de l'Opera," he said.
"We will take it a step at a time. We will look at the Breeders' Cup again."
Joseph O'Brien reported that Kingsbarns had lost his action but is hoping it was just a minor problem.
He said: "When he met the road, he took a bit of a bad step and lost his action. He wasn't too bad pulling up and hopefully he's just given himself a little bit of a bang."