McIlroy, chasing his first major victory in four years, had felt his attacking approach was paying off until his late slips and he intends to play the same way in the last round.
Bad weather and Rory McIlroy have not made easy bedfellows in the past, but the Northern Irishman was stoic under the deluge to lay down a serious marker at Carnoustie.
But Woods admitted he was happy with his round overall.
"Given what happened the last few years, I didn't know if that would ever happen again, but here I am with a chance coming Sunday in a major championship".
Also playing himself out of contention on a day featuring plenty of birdies is Jason Day, who also made 6 at No. 12 and is 1 over after 15 holes.
Woods still walked away today realizing he made it a little tougher on the weekend at Carnoustie if he wants to end a decade without winning a major. He almost sent his tee shot into the burn, avoiding the hazard by a matter of inches. He said his goal was just to hit the green and make a par. He missed an 8-footer on No. 5 for the outright lead.
Tiger Woods is making a bit of a move in the British Open, sinking a long putt on the ninth hole for an opening 3-under 33 on the front nine.
A light rain in the morning that gave way to soft sunlight in the afternoon took some of the sting out of Carnoustie. In this situation the wind stays down and the short-and-straight Simpson pounds fairways and greens to shoot 62 and come from the clouds. "It's going to be a meaty start, not to mention, obviously, the last few holes to finish".
In 2014 McIlroy was the victor of the Claret Jug at a sun-soaked Hoylake, but he refused to let the conditions get to him on Friday in his chase for a fifth major title and first for four years. It matched the Open course record set by Steve Stricker and Richard Green and is the best Open round of Rose's career.
Rather than laying back to 220 on a bunch of medium-length par 4s, Tiger Woods runs back his Saturday game plan as lesser irons players (and weaker minds) wilt in the wind. He is even par for the tournament.
By birdieing six of his first 14 holes while bogeying none, Woods had gone from even par and a crowded tie for 29th place into, temporarily, a tie for first in his first Open Championship appearance since 2015. He thinks that's what may have cost him a tilt at the Masters title in April when he faded in the final group alongside eventual champion Patrick Reed.
Tiger Woods slogged through a wet Friday at the British Open.
Adam Hadwin, Canada's lone entry in the field, shot a 1-under 70 on Friday to make the cut.