Unheralded 27-year-old Castro put his name alongside record holders Greg Norman and Fred Couples with a nine-under-par score on the TPC Sawgrass Stadium Course following a practice round with fellow Georgia Tech alumnus Kuchar.
Seven birdies and an eagle propelled the red-haired nephew of former LPGA player Jenny Lidback of Peru, who held a three-shot lead over Rory McIlroy and Zach Johnson with world number one Tiger Woods a further shot back.
"I played with Kuchar yesterday, which helped because obviously the guy has gone around the course and won," said Castro, a 2011 graduate of the Web.com Tour who has made just seven of 14 cuts on the PGA Tour this season.
Castro, ranked 267th, said there was no single revelation he drew from the practice session.
"Just little things here and there," he said. "It's always interesting to watch what he does around the greens, or any player that's had a lot of success.
"Where he practices his chipping from, putting from," Castro said. "And he's fun. He keeps it light out there. If my attitude would be like Kuchar's more often, it would probably be a little better."
Practicing with Kuchar and Australian Geoff Ogilvy, a former U.S. Open winner, put Castro in the right frame of mind.
"Kuchar and Geoff Ogilvy both are great players, veteran guys. Just kind of got the feel of going about their business and trying to figure out the golf course," he said.
Castro figured out a winning formula, hitting all but one fairway and using laser-like irons to set up six birdie putts within five feet, including four within two feet.
His 13-foot, downhill putt on his last hole for a record-setting 62 slid four feet past the cup.
Castro was so efficient with his irons that he did not have to attempt a single putt over 10 feet in his round.
It was not Castro's first 63 in a PGA tournament.
He posted an opening nine-under 63 at the 2013 Humana Challenge before finishing tied for 37th. A final-round seven-under 63 at the 2012 Greenbrier Classic gave him a tie for seventh for his only PGA Tour top 10.
But Thursday's record-tying round was something Castro could only imagine before putting his lessons into practice, leading a reporter to ask about the dream foursome he listed on the PGA Tour website - Bobby Jones, Tiger Woods and John Lennon.
"I was a big Beatles fan, specifically Lennon," he said. "I doubt he ever even picked up a golf club, but one of the most interesting historical figures, in my opinion."
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- Geoff Ogilvy