For those in pursuit of Clark, they will take comfort in knowing the past six halfway leaders have not gone on to win the title.
And this is the largest 36-hole lead at the US Open since Dustin Johnson led by four the last time it was staged at Shinnecock Hills in 2018, when Brooks Koepka emerged as the winner.
And that this is one of the toughest courses on the planet, where shots can be lost in an instant, as former US Open champion Johnson found to his cost when he posted a quadruple-bogey eight on the par-four 15th.
Fitzpatrick is the only other former champion under par and the Englishman put together a typically tenacious round, with two birdies in his closing three holes lifting him back to where he started the day.
McIlroy was seemingly ready to charge when he too reached three under with a birdie on the eighth but his wedge play cost him dearly.
He misjudged shots on the 10th, 11th and 12th holes, when the gusting wind was at its strongest, with his ball falling off the back of the greens as he posted three successive bogeys.
The 37-year-old responded with back-to-back birdies, but a thinned chip which ran into a bunker, contributed to a double-bogey six on the 15th.
“Even par going into the weekend isn’t terrible. I’m only three back of second place but obviously Wyndham’s built a bit of a lead,” he said on Sky Sports.
Three bogeys on the back nine also curtailed his playing partner Tommy Fleetwood’s progress and left him at one over. Fleetwood finished runner-up here in 2018 when he shot a 63 in the final round after starting it six adrift of eventual champion Koepka.
Scheffler, who is attempting to become the seventh player to complete the career Grand Slam is level with McIlroy, after carding a two-under 68.
The American cut a frustrated figure at times despite hitting 12 out of 14 fairways and 15 of 18 greens. His putting – where he ranked 61st on strokes gained – was his frailty, hindering his ability to climb the leaderboard.
Fitzpatrick’s brother Alex is also at level par on his US Open debut, while his compatriot, the newly crowned US PGA champion Aaron Rai registered a 67 to sit at one over along with Justin Rose and Ludvig Aberg.
Tyrrell Hatton is a stroke back and Scotland’s Robert MacIntyre just made the cut after a second-round 74.
However, two-time US Open champion Bryson DeChambeau missed the cut for a third successive major, while Jon Rahm shipped six shots in five holes on the back nine to play himself out of the weekend.