Thompson shot a 4-under 66 at the treacherous Olympic Club Lake Course, one of only six sub-par scores recorded, and took a three-shot lead at the nation's oldest professional golf tournament.
He lost in the championship match of the U.S. Amateur on this course five years ago and although he has yet to make a splash on the PGA Tour, Thompson has survived the cut 10 times in 15 previous events this year.
Thompson made seven birdies on a course that got the best of some of the world's top players -- Phil Mickelson, Masters winner Bubba Watson, world No. 1 Luke Donald and defending champion Rory McIlroy among them.
It was the latest piece of evidence that Woods is moving closer to the form that made him the best and most feared player in his sport. His two victories this year have advanced him to No. 4 in the world rankings and a win this week would give him 15 major championships, three away from the record total amassed by Jack Nicklaus.
Woods has not won a major title in four years.
Toms is seeking his second major title, his only one to date having come at the 2001 PGA Championship. Watney is going after his first major crown and that bid was helped along Thursday when he holed his second shot from the fairway at the par-5 17th for only the third double eagle in U.S. Open's 112-year history.
The large crowd at even par 70 included an assortment of big names and lesser lights.
Michael Allen, who at age 53 is the third-leading money winner on the Champions Tour this year, was part of the large group at 71. Hunter Mahan and Jason Dufner, both of whom have won twice on the tour in 2012, and Rickie Fowler, who has one victory, were all at 72. Fowler was 1-under through 14 holes, but suffered a late bogey and double bogey.
Woods was paired with Mickelson and Watson for the opening round and easily outplayed them both.
Mickelson's opening tee shot sailed into a tree and was never found, leaving him with a two-shot penalty that started him on his way to a 76. Watson struggled to a 78.
The U.S. Golf Association paired the world's top three players for the opening two rounds and they all had their problems with the Olympic Club.
Third-ranked Lee Westwood had a 73, Donald shot a 79 and McIlroy, who won the event last year with a record 16-under total, finished with a 77.
There were 32 scores of 78 or higher posted.