Can he keep it going? A year ago, the 2007 Masters champion followed up with a 74 in the second round on the way to a ninth-place finish.
"This game demands resilience," Johnson said. "That just comes with experience."
Woods has plenty of experience winning majors he's got 14 of 'em but it's been more than five years since he captured the last one, the longest drought of his career in the tournaments that matter most.
Woods also got off to a strong start, shooting a 69 in the increasingly difficult conditions of the afternoon, but don't get too worked up about his chances just yet.
He shot 67 in the opening round each of the last two years.
He didn't win either time.
The world's top-ranked player yanked his opening tee shot off a lone tree far left of the fairway and was forced to take an unplayable lie, leading to bogey. But a stretch of three birdies in four holes after the turn moved Woods into contention, and he added another two-putt birdie at the par-5 17th after a couple of iron shots that just kept rolling and rolling on the hard ground.
"It was tough," Woods said. "The golf course progressively got more dried out and more difficult as we played. I'm very pleased to shoot anything even par or better."
Rory McIlroy, ranked No. 2 in the world, is still trying to recapture the form he showed last August, when he captured his second major title with a runaway victory at the PGA Championship. At the moment, he's not even close.
The 24-year-old from Northern Ireland has been mired in a baffling slump since changing equipment, and he showed no signs of snapping out of it as he hacked his way to a 79 the second-worst round of his Open career.
The only time McIlroy shot worse was an 80 at St. Andrews in 2010, but that was more a product of a brutal wind than poor shots.
This time, he could blame only himself. Heck, he didn't even beat birthday boy Nick Faldo, who stirred up a bit of a tempest this week when he advised McIlroy to spend more time focused on golf rather than off-the-course pursuits.
Faldo, who turned 56 Thursday, matched McIlroy's score even though he's barely played the last three years.
"I wish I could stand here and tell you guys what's wrong and how to make it right," McIlroy said. "I don't know what you can do. You just have to try and play your way out. Sometimes I feel like I'm walking out there and I'm unconscious."
Z. Johnson -5
D. Johnson -3
A. Cabrera -2
B. Watson -1