Former champion and third-ranked McIlroy made a hash of the back nine to slip to eight over, two outside the qualifying mark, joining notables Phil Mickelson and Rickie Fowler on the sidelines.
Not that the two golfers ranked above McIlroy did much better.
World number one Jason Day of Australia squeezed in at five-over-par with defending champion Jordan Spieth a shot better after a pair of two over 72s.
Johnson was safely in the clubhouse on four-under 136 having completed his second round Friday before embarking on his third round Saturday evening in Pittsburgh.
After the appalling weather which hit the second major of the golfing season Thursday, tournament officials grouped players in threes for the penultimate round, with started on the first and 10th tees in an effort to make up time.
Unheralded Texan Andy Landry was a stroke further back after a second round 71 with Spain's Sergio Garcia, like Johnson chasing the major title his talent surely merits, in a four-strong group on two-under 138.
That group also included France's Gregory Bourdy, who might have joined Johnson at the top of the leaderboard only to fluff a chip on the 18th to make a double bogey and finish with a 67.
Round of the day Saturday came from former British Open champion Louis Oosthuizen of South Africa, a five-under 65 to go to level par and into contention.
For a while it looked as if four-time major winner McIlroy would card a similar score or better as he followed his first round 77 by reaching the turn in four-under 31 to move to three over.
But on the third, his 12th, the Northern Irishman three-putted from close range for a double bogey and his momentum was gone.
He still had a chance of being around for the final two rounds but also double bogeyed the tough ninth, his closing hole, for a one-over 71.
Including fourth-ranked Bubba Watson, who was five over at halfway after a promising start, and Fowler who was a thumping 11 over, the top five in the world were a cumulative 33 over for their two rounds.
U.S. Masters champion Danny Willett of England will also struggle to match his Augusta heroics, trailing Johnson by nine shots.
Johnson will be looking to erase the memory of the 2015 U.S. Open where he missed a three-foot putt on the final hole at Chambers Bay to hand the title to Spieth in a dramatic finish.
He has also finished runner-up at the 2011 British Open and been a strong contender at a number of golf's top four tournaments.