A three-putt bogey on the 18th hole, where he missed a short putt for par, was a frustrating conclusion for Woods but his one-under-par 71 for a four-under total of 140 was a fine score in extremely challenging conditions where the average was over six strokes over par.
"I'm very pleased to be able to shoot under par today. That was the goal, anything par or better today was going to be a great score, and I was able to accomplish that," said Woods.
England's Ian Poulter, who shot a 71, was one stroke back while Northern Ireland's Rory McIlroy (75) and Welshman Jamie Donaldson (73) were both at two under.
Four-times champion Woods made three birdies and two bogeys while hitting 10 of 14 fairways but it was a sign of how tough approach shots were in the swirling wind that he hit only half of the greens in regulation.
He was majestic on the greens on the front nine - he one-putted seven of his first nine holes, including twice for birdie, as he hunted down overnight leader Pettersson.
Woods went close to chipping in for birdie on the par-four ninth when his ball settled agonisingly on the edge of the cup but his luck returned on the next hole where his putt circled the hole before sliding in.
From then, on the tougher back nine, it was a case of damage limitation in winds reaching a peak of 38 miles per hour and the former world number one survived, with a birdie on the par-four 12th the highlight.
"Wow, it was tough out there," said Woods. "You can't take anything for granted, a simple tap-in is not a simple tap-in.
The putter is oscillating all over the place and the ball is oscillating and you have to make an adjustment.
"It was a tough day. I mean, your start lines, Holy Cow, we are starting balls so far off line, to have it come back in. There's so much drift to this wind."
Adding, along with Woods, to the retro-feel of the leaderboard, twice US PGA winner Vijay Singh posted an impressive three-under-par 69 - the only player to score in the sixties.
The 49-year-old Fijian, champion in 1998 and 2004, called on all his experience to handle the difficult coastal conditions.
"Nobody is used to winds like this," three-times Major winner Singh said after mixing five birdies with three bogeys.
"You're contending for a Major but we didn't expect wind like this. These are really strong winds.
"Yeah, I love contending in the Majors, but you just contend with yourself and try to make a score if you can."
Pettersson, who started on the back nine, looked to be the classic 'one-round wonder' with two bogeys in his first three holes but he recovered well with three birdies, including a chip-in from 20 yards on the par-four first.
However, the Swede let his solo lead slip on the front nine with three consecutive bogeys as he ended with a two-over 74.
"I let it slip a little bit but overall I played pretty good. I think two-over today is like two-under yesterday," he said.
Poulter put himself firmly in the frame until bogeying the 18th to fall one shot behind the leaders while McIlroy recovered from four bogeys in his first 13 holes with two birdies to card a respectable 75.
"It took a little bit of adjusting to, I missed a few balls right at the start but I was able to get into it and it was nice to make a couple of birdies," McIlroy said.
Among those whose scorecards were battered by the winds so much they were blown out of the weekend's play were Americans Rickie Fowler and Hunter Mahan, who struggled to matching 80s.
World number four Lee Westwood missed the cut after shooting a 77 to finish at eight over and US Open champion Webb Simpson also headed home with his even-par 72, excellent in the circumstances, not enough to undo his 79 from Thursday.