Chau produced a daring ride on Supergiant ($10) who led all the way to beat Ballistic Boy ($8.50) by a nose in the Gr.3 Gunsynd Classic (1800m).
The favourite Kinane ($1.90) was 1-1/4 lengths back third.
After years riding around the NSW northern rivers Chau decided to switch to the Gold Coast this season where he does much of the riding for Costa.
Costa said he had never considered getting a high-profile jockey even after Supergiant had run second at his previous start in the Doomben Guineas.
"Allan does a lot of the hard work and he deserves his chance. It is his first Group winner and mine too so it is all the sweeter," Costa said.
The winter plans for Supergiant had been the Queensland Derby but when that race was scrapped, Costa made a change.
"Now he can go to the Rough Habit Plate in a fortnight. He will be even better for the effort today," Costa said.
"He is a horse which seems to get fit with racing and that was only his fifth run."
Costa bought Supergiant off a video of a barrier trial after contacting New Zealand Bloodstock agent Phill Cataldo, who had sighted the son of Red Giant running second in a Cambridge trial for trainer Jim Collett.
"Chris Waller's Queensland manager recommended Phill so I owe him a favour," Costa said.
"Supergiant was actually the first horse that Phill put forth to me. I received an email and you never really want to jump into the first one, but I liked his trial and he was priced affordably at $70,000.
"It was always going to be a little bit of a punt for owners given he is by a sire in Red Giant that is not that well known in Australia, but on the back of his trial and reasonable price, we probably could have sold him five times over."
Costa said he knew he had a good horse when Supergiant beat top galloper The Candy Man in an exhibition gallop.
Chau said he believed Supergiant would go on to be a top-class horse.
"He is so tough and showed it again today when challenged," Chau said.
Trainer Chris Anderson was disappointed but not deflated by Ballistic Boy's second.
"The finish was touch and go. Onwards we go and there is always next week," he said.
Kinane passed a vet's inspection after a float incident on the way to the track.He was forced to make a long run after going back from his outside barrier.