However, it was Tiger Woods who dominated much of the talk at Chambers Bay, with the former world number one slumping to a 10-over-par round of 80, the fourth worst round of his career.
Current world number one Rory McIlroy faired slightly better to sit at two-under, while Phil Mickelson's bid for a first U.S. Open title began with a 69.
Stenson started strongly with birdies at the second and third, with a third birdie at the eighth sandwiched either side of bogeys at the seventh and ninth. Having taken the turn in 34, Stenson made his move on the closing holes, with four birdies in five holes from the 14th to the 18th propelling him to five under alongside Johnson.
The big-hitting Johnson took advantage of his length off the tee, to card six birdies and a single bogey.
Having started on the back nine, Johnson birdied the 11th and 12th to take the turn in 33. Four birdies early on his closing nine meant that birdies on his last two holes would equal the low round in U.S. Open history, but a par at the eighth and a bogey four at the par-three ninth saw the record, and the outright lead, slip away.
One back is Patrick Reed who fired a 66, with Matt Kutchar and Ben Martin a further shot adrift on three-under.
World number two Jordan Spieth and Australian Jason Day form part of an eight-man group on two-under.
Three-time major champion Mickelson, who is bidding to complete a career Grand Slam, has finished runner-up at the U.S. Open a record six times and 'Lefty' got off to a strong start, taking the turn in three-under. However, three bogeys and a single birdie on the back nine meant he had to settle for a one-under par 69.
World number one Rory McIlroy is seven shots off the pace, with the Ulsterman unable to make use of the advantage handed to the early starters. McIlroy struggled with his putting technique throughout his round of 72, with the relatively poor putting surfaces on offer not helping his cause.
McIlroy carded two birdies and two bogeys in his opening seven holes and after a run of eight pars, bogeyed two of his last three holes to enter the clubhouse at two-over.
Paired with Rickie Fowler and Louis Oosthuizen, Woods and his playing partners endured a day to forget, with the trio posting a combined total of 26-over-par.
It was hard to watch Woods on Thursday. A player a shadow of the man who once dominated golf, the American produced some of the day's worst shots as his struggles off the tee continued.
But it wasn't only off the tee that Woods battled, with a missed five-foot putt for par on the sixth and topped iron on the final hole just two examples of an all-round struggle.
Woods bogeyed three of the first four holes, with a bogey at six seeing him take the turn in 39. It didn't get any better on the back nine, with a run of three bogeys from the 11th to the 13th followed by a double-bogey at the 14th.
A birdie at the 15th was a very rare bright spot, with a another dropped shot at the 18th an unfortunately fitting end to Woods' day.
Matters were even worse for Fowler who finished on eleven-over. The only man standing between Woods, Fowler and the bottom of the leaderboard was club pro Rich Berberian Jr. who carded an 83.