Last month's Musidora Stakes winner simply blew the opposition away in the final furlong to give Dettori a sixth Oaks triumph.
Sent off at 11/2, Snowfall had the race won before the furlong marker and crossed the line a record 16 lengths clear of the George Boughey-trained 50/1 chance Mystery Angel in second place.
Divinely (20/1), also trained by O'Brien, was a further length and three-quarters way in third, with Save A Forest (40/1) fourth and the O'Brien-trained 5/2 favourite Santa Barbara only fifth.
Mystery Angel was well away and stayed in the front rank throughout the race. Sherbet Lemon was alongside her in the early stages with La Joconde, Willow, Dubai Fountain and Saffron Beach on their heels.
The field moved over the stands side after turning Tattenham Corner, with Dettori able to steer a clear passage for Snowfall.
Hitting the front two furlongs out, the daughter of Deep Impact continued to put daylight between herself and her rivals to become one of the easiest Oaks winners ever seen.
O'Brien said: "We really thought she was a proper Group One filly last year, and she kept disappointing. Little things happened to her in races, and stuff like that.
"But she won the Musidora very impressively. You're never sure, but she has a lot of class - when ground turns like that, you can sometimes get extreme distances.
"But Frankie gave her a very good ride - and she looks a very special filly, doesn't she?"