That birdie took Woods to six-under, within range of Australia's clubhouse leaders Adam Scott and Jason Day, who are alongside British Open victor Francesco Molinari, three-time major victor Brooks Koepka and Open champion Louis Oosthuizen, at seven-under par.
A stunning eagle launched Australian Adam Scott past countryman Jason Day into the outright lead at the Masters, before a three-putt on the next hole brought him back as rain lashed a weather-interrupted second round. He played the first eight holes at even par before kicking it into another gear, starting with a 37-foot birdie putt on No. 9.
Woods had played a sublime recovery shot from the pine straw immediately prior to that incident and duly converted his resulting birdie putt before picking up another shot at the 15th to get to six under.
The Queenslander, who received medical treatment on course beside the second hole on Thursday, came out firing on Friday with a round of 5-under par, rocketing him to seven under. Simpson made a 37-foot putt for eagle on No. 13.
But after producing a miracle recovery shot to find the green, Woods was almost taken out in sensational fashion by a security guard who slid in, after slipping on the mud caused by earlier rain while rushing to protect the superstar.
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He also shared his intentions to now shift his focus to the community and help players develop their basketball skills. Johnson, a huge ambassador of the game, brought prestige with him and the promise of that prestige returning.
"It is what it is", Woods said.
"It's a bunched leader board ... if someone decides to break away on the weekend I'm in a good spot to run with them".
Woods then managed to make a miraculous birdie from out of nowhere to put himself right into the thick of the action.
McIlroy was also less than happy with his tee shot on the par-three fourth, but holed from 32 feet for an unlikely birdie, only to then drop shots on the sixth, seventh and ninth, where his approach plugged in the top of a greenside bunker.
Yet Woods provided the day's biggest talking point, as he surged into contention having survived a dramatic scare on the 14th hole when a security guard - running in a bid to control spectators - slipped and nearly knocked golf's biggest star off his feet. He still was within four shots, along with Justin Thomas, who had a 68.
He didn't show any trouble the rest of the way, and didn't find much interest in talking about it after his round except to say "accidents happen" and "it's all good".