Zach Johnson, Kevin Na and Matt Kuchar were knotted at eight-under 136, a shot clear of compatriot Harris English.
But with five players sitting a further stroke adrift and the course likely to get tougher over the weekend, the event widely known as golf's unofficial fifth Major remains wide open.
One player who will not be able to make a move on Saturday is McIlroy, who has had a miserable record at the TPC Sawgrass course where he also missed the cut in his previous two appearances at the venue before skipping the event last year.
The Northern Irishman, who had not missed a cut since last year's Wells Fargo Championship, carded five bogeys and one birdie on Friday for a two-day total of 148.
"There is something about this place I just can't get to grips with," McIlroy said. "I just need to try and get the hang of this golf course somehow, it's just - I find it pretty difficult but it's just one of those weeks."
Woods had to fight to avoid missing successive cuts for the first time in his professional career after shooting a 74 in his opening round.
The former world number one, who failed to make the weekend at Quail Hollow last week, rose to the challenge by posting a 68 that included a string of four birdies around the turn that put him clear of trouble.
"I probably could have gotten one or two more out of it but I really played well today. I was just very consistent and nothing spectacular, just real solid golf," said the 14-times Major champion.
It was a fair description of a round which leaves Woods six shots off the lead in a tournament he won in 2001.
Johnson, the 2007 Masters winner, got off to a great start with three birdies in the opening four holes but he will be disappointed to have ended with a bogey on the 18th for a six-under 66 that tied for the lowest round of the day.
"I never really gave the golf course much - in other words, I kept it where you need to keep it. My misses were proper. I was aggressive when I could be aggressive, and I caught a couple nice saves in there, too," said the 36-year-old.
"But when you shoot that kind of score around this golf course any day in the year, or any week, you're putting well. Clearly that's what I've been doing the best."
Martin Laird, who shared the overnight lead with fellow Briton Ian Poulter, slipped two shots off the pace after carding a 73, his solid effort undone by a double-bogey at the 'island green' 17th, where he found water, and then a bogey on the 18th.
Poulter opened his second round on the back nine with a double-bogey on his first hole, the 10th, followed by another double at the par-three 13th.
However the fashion conscious Englishman recovered to card a four-over 76 that left him five strokes off the lead.
Defending champion K.J. Choi of South Korea missed the cut after a 76 on Friday left him with a two-day total of 151.
Also heading home early were British Open champion Louis Oosthuizen, who was beaten in a playoff by Bubba Watson at this year's Masters, American world number five Hunter Mahan and three-times Major winner Padraig Harrington of Ireland.
American Steve Stricker ended his run of 49 tournaments without missing the cut.