Cox and Kirby follow up victory of Golden Horde from 12 months ago.
Supremacy lived up to his name with a dominant display in the Qatar Richmond Stakes at Goodwood.
Sixth on his Windsor debut in mid-June, Clive Cox's youngster showed the benefit of that initial experience with a facile victory at the same venue earlier this month.
The Mehmas colt looked to have plenty on his plate stepping up to Group Two level, with a lofty standard set by William Haggas' Windsor Castle and July Stakes runner-up Yazaman, but Supremacy proved more than up to the task.
Ridden by Adam Kirby, the youngster was quickly away from the stalls, which allowed him to move across the track from his wide draw and grab the rail.
Challengers were queuing up racing inside the final two furlongs – but the further Supremacy went the better he looked and he was good value for the winning margin of four lengths.
Yazaman was under pressure some way from home, but boxed on to finish second again, just ahead of Lauded in third.
Cox was landing the Richmond Stakes for the second year in succession, having struck gold with subsequent Commonwealth Cup hero Golden Horde 12 months ago.
Kirby said: "It wasn't (the plan to get the rail) at all. That just seemed to happen. I wanted to get him out and get him in gear as he's a big, long-striding horse and once he gets into that stride, he covers a lot of ground. He's a horse I think a lot of.
"It was his speed that brought me to the front, which then allowed me to get the rail and give him a breather and fill himself up.
"He's got a bit of scope, so he will definitely train on. He's a big, long-striding horse and he's got a great personality, he's chilled out and takes these races day by day.
"I was really pleased with his attitude, he didn't get hyped up, worried or feel on edge. I really like him, I think it was a really smart performance."
Cox is delighted to unearth another high-class juvenile, having last month saddled 150-1 shot Nando Parrado to land the Coventry Stakes at Royal Ascot.
Cox said: "We knew he was nice, but he was very green first time. He has been a wonderful horse to deal with and won in a very fast time at Windsor.
"This was soon enough and in a perfect world I was hoping we had another week or two, but he has done that so well. He has bags of speed and the way he finished that race after going so fast was amazing.
"I think Golden Horde was a bigger horse at this stage of his life and what he did last year was amazing. Clearly he has progressed as a three-year-old, winning the Commonwealth Cup.
"This fellow is only just getting going. I think he is very high class and we will just think about that one (where he goes next). The timing is always important as always, but he is top-class."