The world class leaderboard also included US Open champion Webb Simpson, US Ryder Cup players Steve Stricker and Hunter Mahan in a group with Woods another shot back on 67, but it was Web.com graduate Castro who stole the spotlight.
Staging a clinic with his irons to receptive greens, Castro, ranked 267th in the world, made seven birdies and an eagle to match the mark shared by Greg Norman and Fred Couples in his debut on the Stadium Course at TPC Sawgrass.
"It gives me proof that when you play great, you're good enough," Castro, 27, said about the confidence boost he gained from a brilliant round that set the bar in the morning wave.
Castro's playing partner, Jason Bohn, said he had never seen anything quite like the red-haired American's round.
"Ultra impressive," said Bohn, who shot a four-under 68.
"I've never seen a 63 shot like that. His iron play was like a clinic, he had so many kick-ins. That's the highest score he could have shot. He was awesome."
Castro had six birdie putts within five feet, including four within two feet and did not make a single putt of more than 10 feet in his 63.
World number two McIlroy also took advantage of greens softened by last week's heavy rains to reverse a trend of poor results for him at Sawgrass, where he had never broken par or made the cut in three prior appearances in the tournament.
Top-ranked Woods, the 2001 winner, led the way among the afternoon starters, making four consecutive birdies from the ninth hole and adding another at the 16th and appeared poised to tie for second on 66.
But Woods's approach aimed at the back right pin at 18 trickled over the edge of the green and down a slope. He hit a weak chip that hung in the fringe and needed two strokes to get down, ruining his bid for his first bogey-free round at Sawgrass in 56 tries.
Woods was pleased with his round.
"I made a couple key putts here and there, and I really took care of the par-fives. I birdied all of them today, which is nice," said Woods, the only three-time winner this season.
Also in the group that included Woods was Casey Wittenberg and Ryan Palmer, with Bohn and Swedes Henrik Stenson and David Lingmerth, Australian Greg Chalmers, Ireland's Padraig Harrington and Spaniard Sergio Garcia another shot back.
Castro, whose best US PGA Tour finish is a tie for seventh at last year's Greenbrier Classic and whose best result this year is a tie for 16th at Phoenix, gained a jolt of momentum as he finished his opening nine.
Starting on the back nine, he made the turn in five-under 31 with birdies on each hole of the challenging finishing stretch called "The Gauntlet."
He two-putted the par-five 16th from 65 feet, tapped in at the par-three 17th island green from 19 inches and at the par-four 18th from 23 inches.
Castro eagled the par-five second hole after hitting a three-iron inside four feet for sole possession of the lead. He followed that with birdies from 21 inches at number four and from 18 inches at the sixth.
"I hit it close a lot," said Castro, whose aunt, Jenny Lidback, played on the LPGA Tour and whose family on his mother's side comes from Peru.
Hitting it as close as possible at the par-three eighth hole that was playing 233 yards was Michael Thompson, who made the only ace of the day with a perfect three-iron.
Castro set up his irons with his own accuracy off the tee, hitting all but one fairway. He had 10 one-putts and 26 putts in all.
Defending champion Matt Kuchar was eight shots off the pace after opening with a one-under 71, while four-times Major winner Phil Michelson was a further shot back after mixing four birdies with two bogeys and a double-bogey.