Scheffler’s score was deceptively good on a day when gusting winds reached 40mph and ensured that the greens became firmer and even more perilous.
Only one other player, Argentina’s Emiliano Grillo – who moved to level par for the championship after signing for a three-under 67 – broke the par score of 70.
It was attritional. As US Opens often are. Ten players began the day under par. By the end, there were only five.
The third-round scoring average was 73.61, the highest of the championship.
It took one hour and 50 minutes for the first birdie to be registered, one of only two in 70 combined holes played by the field over the opening two hours.
Scheffler’s performance was all the more impressive given he bogeyed the first two holes and his resurgence arrived entirely on the harder back nine.
A birdie on the 10th provided some impetus but his chip-in on the 14th followed by an outpouring of emotion signalled a shift in momentum.
Further birdies at the 15th and 16th helped him play the final nine holes in 32 shots, matching the lowest score of the week.
But Clark’s lead was barely threatened.
Unheralded American Stevens briefly got within two shots at four under par but he was one of several players whose challenge faded on the back nine.
Rory McIlroy was another. The Northern Irishman had a hat-trick of birdies from the fifth, one of which was a sensational 66-foot putt, to get to two under but five bogeys in his closing nine holes derailed his title hopes.
And Fitzpatrick’s hopes of adding to his 2022 US Open triumph were all but sunk by a ruinous run of three successive bogeys to start his round.
The normally unflappable Yorkshireman, playing in the final group with Clark, had started four back at three under but by the final hole his frustration was evident after he hacked out of deep rough and then overhit a chip. It led to a fifth bogey of the round as he finished eight off the pace.
Those at one under know they need to shoot low on Sunday and hope Clark makes mistakes.
Perhaps they will follow Fleetwood in taking inspiration from the last US Open held at this Long Island layout when the Englishman shot a 63 in 2018’s final round as he came from six back to finish one behind champion Brooks Koepka.
Fleetwood, who will start eight adrift said: “We’ll see what conditions bring. It’s nice when you have good memories of a place, isn’t it? I have great shots to go off and good feelings, so you know, I can draw on that.”
But equally Clark knows that if he can emulate the only three players to have finished under par at a Shinnecock Hills US Open – Ray Floyd in winning in 1986, and champion Retief Goosen and runner-up Phil Mickelson in 2004 – then the title is likely his.