Castro, a second-year member of the PGA Tour who has only one Top 10 finish in his brief career, shot a 9-under 63 at the TPC-Sawgrass course to grab a three-shot lead after the opening round of golf's most lucrative event.
Castro eagled the par-5 second and did not suffer a bogey on a mild, calm day in which 67 players in the 145-man field broke par.
McIlroy, who had never shot under par on the course before and who missed the cut in his other three appearances at this tournament, fired a 66 to share second place with Zach Johnson.
Woods, ranked No. 1 in the world in front of McIlroy, was in the group at 67 after suffering a bogey at the closing hole. Woods turned in his lowest first-round score in 16 trips to The Players, recording birdies on all four of the par-5 holes.
Vijay Singh, who sued the PGA Tour earlier this week concerning its investigation into his admitted use of deer antler spray, posted a 74.
McIlroy birdied five of the first eight holes to create his excellent round.
"It was benign out there," McIlroy said. "There wasn't much wind. It was perfect conditions for scoring and I was able to take advantage of those."