He missed a cut for only the ninth time in his PGA Tour career, and for the third time in a tournament following a victory.
After winning last Sunday at Congressional, Woods was on a course he'd never seen before.
“I didn't quite have it,” Woods said. “I drove it really good today and I just did not have the feel for the distances. The ball was just going forever.
I know we're at altitude, but I just couldn't get the ball hit pin high no matter what I did, and subsequently, I made some bogeys.”
Phil Mickelson also failed to advance to weekend play, the first time Woods and Mickelson have missed the cut in the same tournament as professionals.
Mickelson shot his second straight 71.
U.S. Open champion Webb Simpson topped the leaderboard at 9 under when play was suspended because of darkness in the round that was delayed because of rain.
Simpson made a 6-foot birdie putt on the par-3 18th for a 4-under-66.
A dozen players were unable to complete the round.
Woods believes his distance control will be easy to work on heading to the British Open, which starts July 19 at Royal Lytham and St. Annes.
“It's not going to be this warm and we're not going to be at altitude. We'll be on the beach,” he said.
After the rain delay, Woods had bogeys at Nos. 10 and 11 to fall to 3 over, then made three late birdies but missed two other tries from inside 12 feet.
The other times that Woods followed a win with a missed cut came in 2005 at Disney and in 2009 at the British Open. Both those times he took a week off after his wins.
When Woods was an amateur, he and Mickelson missed the cut in the 1993 Byron Nelson.
Mickelson had focused more on golf at this year's tournament after taking advantage of the resort's numerous amenities with his family last year. The result was the same.
“I really enjoy the golf course,” he said. “I certainly struggled a little bit on the greens both years, but nothing that should have led to these scores.”
He has gone seven consecutive rounds over par and hopes his game improves.
“I certainly am looking forward to links golf,” Mickelson said. “I enjoy playing the ball on the ground and hitting it—you know, trying to keep it below head high on some tee shots and so forth.
That was fun last year when we had some terrible weather. And it will hopefully play to one of my strengths, which is short game, and I'll try to get that sharp heading into the British.”
Simpson led last year's Greenbrier Classic with nine holes left in the final round before fading to a tie for ninth.
“I was confident last year, I'm confident this year,” Simpson said. “I don't think a whole lot has changed. I learned a lot about myself in the final round last year.”
Simpson had four birdies in a bogey-free round. Two of the birdies came after the rain delay.
Among those still on the course when play was stopped by darkness was Martin Flores, who was a stroke back at 8 under with two holes left.
The round was delayed more than two hours earlier in the day because of thunderstorms.
Rookie Charlie Beljan (62), Jonathan Byrd (68), Jeff Maggert (68) and Jerry Kelly (66) also were 8 under.
Beljan had his career-best round, carding five birdies over seven holes before making before a bogey on his final hole, the par-4 ninth.
His best finish this year is a tie for 29th two week ago in Connecticut in the Travelers Championship.
“Today was the best day of my career,” said Beljan, making his first visit to a PGA Tour media room. “I look forward to the weekend. I'm sure it's going to be a zoo.”
Being near the top of the leaderboard certain fits Beljan's philosophy of a high-energy life. One of his goals is to be strapped to the wing of a biplane in flight.
Another is to ride a motorcycle in the Isle of Man TT Race.
“I like getting my heart beating,” he said. “I like the adrenaline.”
Byrd has been battling illness the past three weeks.
“They always say beware of the sick golfer or the injured golfer,” Byrd said. “I would rather be feeling healthier.”
First-round leader Vijah Singh shot 74 to drop six strokes back.