Once Moore asked the Ed Dunlop-trained filly to step up the pace, the response was instant and she stormed into the lead over a furlong out.
Miss Jean Brodie, a 33-1 shot saddled by Joseph O'Brien, stayed on well to snatch second place.
Lady Lupus (66-1) finished third, with Meeznah (6-1) coming home in fourth in the one mile and four furlongs contest.
The start was delayed while Miss Jean Brodie was re-plated, but once the Classic got underway the Aidan O'Brien-trained Ice Empress set the early pace.
She soon had the field well strung out and was still at the head of affairs with half a mile to run.
O'Brien took Lady Lupus to the front at the turn for home with Akdarena and Meeznah close, but Snow Fairy had made eye-catching progress from midfield.
She quickly burst clear and stamped her authority to win by eight lengths.
Dunlop, winning the race for a third time, said: "It was pretty spectacular really, the way she put the race to bed.
"She is stronger than she was at Epsom and she has a huge heart. The Yorkshire Oaks is a possibility now."
Hibaayeb, the 100-30 favourite, was in mid-division under Frankie Dettori, but weakened quickly on the rain-softened ground from over three furlongs out and finished last.