Volpe Veloce extended strongly to snatch the lead before holding off the fast finishing Packing Eagle with Volks Lightning narrowly third from a gallant Start Wondering.
"This means the world to me," said Bayliss.
"Limited opportunities have stopped me getting success like this, but I've been working hard since I came to New Zealand.
"I've tried to put my best foot forward and Graham Richardson has stuck by me in a big race like this.
"I'm now a Group One winning jockey, but I just can't explain the feeling."
Emotions were running high in the Ellerslie birdcage as Richardson and co-trainer Gavin Parker waited with the mare's large group of owners for the pair to make their winning return.
"It's amazing isn't it," said Richardson. "She deserves it, the owners deserve it and so does Gavin Parker.
"He's done an enormous job, along with the staff, so congratulations to everybody."
Richardson admitted the victory had special meaning after he emulated his first win in the race with Kailey back in 1997.
"I won it 21 years ago and I have had a couple of seconds, so this means the world to me," he said.
"We're going to celebrate today and then bring on the Telegraph.
"We might even go to the Newmarket in Australia as Jake seems to think she is up to it so after a run like that, on ground she doesn't handle, who knows."
The victory took the mare's record to 10 wins from just 13 career starts and she remains unbeaten at Ellerslie with four wins from four starts as well as at the distance where she is six from six.
She will now tackle the Gr 1. JR & N Berkett Telegraph (1200m) which will be held at Trentham on January 20. – NZ Racing Desk.