Mickelson, who has finished runner-up a record six times, was among the early starters and took advantage of flat calm conditions to reach the turn in three under par.
However, the five-times major winner then carded three bogeys and one birdie on the back nine to card an opening 69 and finish one under par, four shots behind compatriot Johnson and Swede Stenson.
Mickelson’s score was matched by Colin Montgomerie who put in a dogged performance to stay under par during his opening round. The former European Ryder Cup captain, who has won three major titles since entering the Seniors Tour, made an encouraging start with a birdie at the opening hole and added three more along with three bogeys in his round of 69.
Fellow Scot Marc Warren reached the turn two under after birdies as fourth and fifth, but successive bogeys brought him back to level par, before he picked up shots on the 15th and 18th as he finished one ahead of his compatriot on 68.
Mickelson declared himself pleased with his opening effort.
“I played well,” he said. “I had a really nice round going and then made bogey on 13 and 14.
“I think the 13th is the hardest approach shot into the green. I did not leave myself the best shot and was way too far back and then made a good bogey on the next.
“[But] no complaints. I’m under par in the first round of the US Open and I am pretty pleased. I thought it was a very fair test.
“The set-up was good. I think everyone in the field is going to struggle with three to eight-foot putts when they are downhill because you can’t hit it hard enough to hold the line and there is a lot of wiggle.”
Mickelson had looked in trouble on the opening hole, missing the green to the left and seeing his ball roll down a steep slope onto the adjacent 18th fairway.
However, the 45-year-old – who celebrated his birthday on Tuesday – displayed his renowned short-game skills by pitching to within inches of the hole to save par, in stark contrast to playing partner Bubba Watson who attempted to “putt” from a similar position with a fairway wood, failed to reach the putting surface and saw the ball roll back to his feet.
Mickelson birdied the third, fifth and eighth before dropping his first shot of the day by three-putting the tenth from long range following a poor approach from a fairway bunker, but bounced straight back with a birdie from 12 feet on the next.
After surprisingly opting to lay up on the short par-four 12th rather than attempt to drive the green, Mickelson had to settle for par there and then bogeyed the 13th and 14th after finding sand on both holes. Johnson had started his round on the back nine and carded birdies at the 11th and 12th before picking up further shots on the first, fourth, fifth and seventh.
The 30-year-old ruled himself out of the Ryder Cup last year by taking a lengthy break from the game to deal with “personal challenges”, prompting allegations in the United States of a positive test for cocaine – claims which have dogged him for several years but which he has always strenuously denied.
Johnson again dismissed the drug claims in his first interviews since the announcement earlier this year, revealing his battle had been with alcohol, and overturned a five-shot deficit in the final round to win the WGC-Cadillac Championship in March.
Johnson was tied at the top of the leaderboard with Stenson, who carded three birdies in a row from the 14th.
The Swede recorded seven birdies in total, along with two bogeys, on the 6th and 8th.
Ryder Cup rival Patrick Reed finished four under on 66 after six birdies and four bogeys.
US Ryder Cup player Matt Kuchar had four birdies and one bogey in a three-under-par round of 67.
World No 1 Rory McIlroy was struggling on the greens as he stood at one over par with two holes to play.