Ozzmosis bounced back from the first defeat of his career in the Group 2 Roman Consul Stakes (1200m), when he finished third behind King's Gambit, to make it four wins from five starts.
The Darby Racing-owned colt, a $250,000 buy at last year's Magic Millions Gold Coast Yearling Sale, started $18 and scored by 1-1/4 lengths from I Am Unstoppable ($6), who finished a head clear of Golden Slipper winner Shinzo ($4.60).
Baker was thrilled to be back in the Group 1 winner's stall on Derby Day, 13 years after combining with his father Murray to win the Derby with Lion Tamer, and was full of praise for Ozzmosis.
"I was here 12 years ago as co-trainer of Lion Tamer with my father and that is one reason I came to Australia," Baker said.
"It is the lucky country and the greatest racing in the world.
"This horse has been outstanding from the first gallop he had. He just put his hand up. It didn't work out last time (but) we were confident we had him right.
"I was very confident he'd run well but it is hard to be confident coming here."