Malibu (gr. I) on Dec. 26 at Santa Anita as near-term goal.
"It wasn't a hard race on him at all," Byrne said. "He kind of toyed with the opposition, but it was a good time and I was happy to see him relax early in the race."
Byrne nominated Eugene's Third Son to the Malibu, the first race in Santa Anita's Strub Series, when he was in California last week to run stablemate Ethan Man in the Breeders' Cup Sprint (gr. I).
Also considering the Malibu is Sprint (gr. I) winner Cajun Beat, who is stabled one barn away from Eugene's Third Son. Cajun Beat, now trained by Steve Margolis, defeated Byrne's colt in a Gulfstream Park allowance in late January.
"I told my good buddy Steve that we'd split a plane on the way out there," said Byrne. "I'd love to take him on at seven-eighths."
The win improved the career record of Eugene's Third Son to 3-3-0 in six races with earnings of $283,445.