But the four-time major victor McIlroy struggled to the turn in 42 as the marquee group combined to play the back nine in 15 over par with just two birdies between them.
This is the second straight year he is No. 1 at the U.S. Open, ending a streak of six straight years with a different No. 1 at this major.
"It's frustrating because I'm hitting the ball well, " he said.
After Woods set the putter down behind his ball on the 10th green, he backed away when the ball moved. That dubious distinction belongs to J.D. Tucker, who shot a 157 in the first round of the 1898 U.S. Open. Just find a happy place and stay there, because I knew it was going to test me to the limits today. I hit two bad putts on one and two, and for most of the day I just didn't putt well. I enjoy the fight.
His worst two shots of the day came on the next hole, where he played from side to side and had a tough up and down to try and save a bogey - which he didn't.More news: China ‘ready to hit back’ at Donald Trump’s tariffs
Tiger Woods hits out of the bunker on the 11th hole on Thursday. "This golf course is kind of setting up for that right now".
Only four players of the 156-man field broke par - world No. 1 Dustin Johnson, fellow-American Scott Piercy and Russell Henley and Englishman Ian Poulter - but even they had hardly conquered the beast at one-under par 69.
In one stretch, Gregory - the 2016 British Amateur champ missed the cut in last year's US Open while still an amateur -double-bogeyed three straight holes. "I feel like I've been playing really solid all year, I feel like I scored really well".
Even being 4-over after two holes, Spieth figured even par would be a reasonable start on a day like this, a course like this. Dustin Johnson returned to No. 1 in the world by winning the FedEx St. Jude Classic. Then he replaced the ball and made the putt for par. The four putts led to a crushing double.
"I was anxious about running the (first) putt by, left it short, blocked the next one, then blocked it again", said Woods, who added another double at 14.