Holmes took advantage of surprisingly calm conditions to fire a flawless, six-under-par 66 in the opening round of the tournament widely considered the "fifth major" by the players.
Britain's Luke Donald rolled in a six-foot birdie putt at the last for a 67 to share second place with Americans Jason Bohn, Ben Crane and Heath Slocum.
Masters champion Phil Mickelson, who could replace Woods as world number one for the first time if he wins this week, opened with a 70 at the TPC Sawgrass.
With hardly a breath of wind on a hot and humid day, Holmes reached the turn in three-under 33 before picking up further shots at the 14th, 16th and treacherous par-three 17th.
"It was a fun day, one of those rounds where everything was going pretty good," the 28-year-old told reporters.
"I wasn't in too much trouble at any point ... one of those rounds where it's not easy but it kind of felt pretty easy."
American left-hander Mickelson, who would take over at the top if he wins on Sunday and Woods finishes outside the top five, was reasonably satisfied after scrambling his way to a 70.
"Shooting 70 today isn't the round that you want," the world number two said after recording four birdies and two bogeys. "There wasn't much wind, the greens were receptive, and there were a lot of low scores.
"The reason I think this was a good day for me is I just didn't have it ... and yet I was able to shoot a couple under par. If I can come out tomorrow, get hot and shoot something in the mid-60s, I can get back in the tournament."
Woods, who missed the cut at last week's Quail Hollow Championship after a surprisingly inept performance, made a reasonably solid start after being warmly applauded on the first tee.
He parred the opening hole after hitting a superb second shot from pine straw well left of the fairway and narrowly missed a birdie opportunity at the par-five second where his attempt from five feet horseshoed out.
Woods, champion here in 2001, struck a good tee shot to 15 feet at the par-three third but again missed the birdie putt and did well to save par at the fourth after his approach ended up in a greenside bunker.
Having recently returned to golf after a self-imposed break of five months following revelations about extra-marital affairs, Woods received several early words of encouragement from the fans at Sawgrass.
As he walked off the second tee, a woman in the gallery called out: "Tiger, remember your dad's with you", referring to the late Earl Woods. The world number one turned his head toward her and smiled.
