A field of 11 juvenile fillies went to post for the Group Two contest and O'Brien was double-handed, with Fleeting the apparent second string behind the Ryan Moore-ridden Peach Tree.
The latter was on the pace throughout before fading, while the trainer's son, Donnacha, settled 12-1 shot Fleeting towards the rear before angling wide to throw down his challenge on the far side.
The hat-trick-seeking Star Terms was in front racing inside the final furlong, but Fleeting saw out the straight mile best to get up and score by a length and a half.
Star Terms galloped on for second, ahead of Sand Share in third, but Dubai Beauty, the 11-8 favourite following an impressive debut at Newmarket last month, was bitterly disappointing.
Paul Smith, son of part-owner Derrick Smith, said: "Donnacha said she was a bit fresh going down to the start, so he took his time with her and in hindsight with that headwind that was probably a good thing.
"She came through horses really well and we're really happy with her. I suppose there wasn't much between her and Peach Tree from her last piece of form and it was a very pleasing effort."
He added: "She got the mile well. We'll look at the Fillies' Mile and the (Prix Marcel) Boussac. They will have to be on the radar now.
"Donnacha was very pleased with her. She picked them up nicely and showed a good temperament. We're happy."
Richard Hannon said of runner-up Star Terms: "She travelled very well, settled and she looks like a very good filly. We'll see where we go from here. We'll regroup, very pleased."
Ralph Beckett, trainer of third home Sand Share, said: "I'm very pleased with her. It was a good effort first time on the turf.
"She's a big old girl and will improve for a winter on her back, so we'll see where we go from here. I couldn't be happier. I'm not sold on the Fillies' Mile. She might go into Listed company next. We'll see."