The American was among many who played both their first and second rounds on a calmer Friday and he followed a three-under 67 with a 69 to reach four under.
Spain's Sergio Garcia shot a 70 in round two to stay two under at halfway, alongside American Scott Piercy (70).
Andrew Landry led on four under after round one but is scheduled to start his second round at 12:11 BST on Saturday.
However, Saturday's tee times could change because the light faded with 27 players unable to complete their second rounds.
England's Lee Westwood, who posted a three-under 67 when he completed his first round early on Friday, is, like Landry, among half of the field who are scheduled to play their second and third rounds on Saturday.
Northern Ireland's Rory McIlroy, Masters champion Danny Willett, Scotland's Russell Knox and Ireland's Shane Lowry will also play their second rounds on Saturday.
Lowry had a two-under 68 in round one while Knox had a level-par 70.
Willett had a 75 and is flirting with the cut as he is tied for 56th with McIlroy the wrong side after a seven-over 77 left him tied for 94th with the top 60 plus ties making the cut.
The world number three, who won the US Open in 2011, told BBC Sport he would "need a 66" to get back in contention on Saturday.
Johnson, who had a putt to win last year's US Open but took three to hand the title to Jordan Spieth, followed his bogey-free opening round with another nine holes without a dropping a shot.
Starting on the 10th, he birdied the par-three 13th to go to four under but gave that back with his first and only bogey of the tournament so far on the first.
A birdie on the sixth, after several missed opportunities, was reward for a disciplined and patient round and he parred his way in to finish just before sunset.
"I'm in pretty good shape, so the physical part's no problem," said Johnson after completing 36 holes in a day.
"But mentally you've got to make sure you stay sharp all day, because you can't go to sleep on any shot out here.
"I hit so many good putts today that I thought were going in, and burned the edge or lipped out. That's just how it goes, these greens are tough."
Johnson's playing partner Garcia started his second round with a bogey-five on the par-four 10th but a birdie on the 17th saw him get back to two under par.
However, bogeys on the 18th and first dropped him back to level par but birdies on the second and sixth kept him in the hunt for his first major.
The Spaniard, who is not renowned for his ability with the putter, made a superb scrambling par with a 50-foot putt at his last hole, the ninth.
Westwood is the leading Englishman but he is yet to play his second round and is scheduled to tee off at 13:28 BST on Saturday.
Andy Sullivan was among those to play 36 holes on Friday and he followed his first-round 71 with a two-under 68 to move to one under.
He played his first nine holes in three under par and said on Sky Sports: "I was aggressive and it paid off. I hit the driver really well, which opened up the greens and I had lots of birdie chances."
Compatriot Lee Slattery was one over for his second round and three over for the tournament after nine holes but two birdies and an eagle on the back nine helped him post a two under 68 to get to level par.
"Adapting to the change in the greens was important as they got faster," he said. "It doesn't matter if it's up hill, downhill, side hill. Every putt is quick.
"I'm so tired that I don't really know what's going on. It's been a really tough day around a very tough golf course. It's been mentally demanding."
Oakmont is generally regarded as one of the toughest golf courses on the US Open circuit - Angel Cabrera's winning score the last time the Pennsylvania course hosted the tournament in 2007 was five over par.
However, Daniel Summerhays made a mockery of that with the lowest round of the opening two days, a stunning five-under-par 65.
The American had two birdies and two bogeys on the front nine but came home in 30 to move up to one under.
"I'm absolutely thrilled," he said. "I was waiting for four days to find out if I had qualified.
"Then I found out I had to play 36 holes in a day but I'll take that."
We've launched a new BBC Sport newsletter ahead of the Euros and Olympics, bringing all the best stories, features and video right to your inbox. You can sign up here.
Dustin Johnson holds the clubhouse lead midway through the second round of the storm-delayed US Open at Oakmont.