Clark, who claimed his second US Open title in four years with a one-shot win over Sam Burns at Shinnecock Hills on Sunday, bagged a seven at the par-four 12th after an errant tee shot led to a drop and he then picked out a bunker before missing a seven-foot putt.
The 32-year-old notched birdies either side of that nightmare hole, while gains at 15 and 17, after an earlier one at six, saw Clark sign for a two-under 68, leaving him five shots behind first-round leader Eric Cole, whose blemish-free, seven-under 63 included an eagle at 13.
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Fitzpatrick - who has won three times so far in 2026, solo at the Valspar Championship and RBC Heritage and alongside brother Alex at the Zurich Classic of New Orleans - carded a six-under 64, recording seven birdies around one bogey and missing just one fairway.
The former US Open champion, who operated with a new driver, is in a group of six players one shot off Cole, which also features Scheffler, Ben Griffin, Kristoffer Reitan, Bud Cauley and Nicolas Echavarria.
Fitzpatrick said: "I played really solid. I took advantage of the scoring holes there."
Scheffler - tied fourth at the US Open last week, four shots adrift of Clark - posted a flawless 64 on Thursday at TPC River Highlands, with four gains on his front nine and two coming home.
Fitzpatrick's compatriots Rai and Rose are two back from Cole, with their five-under rounds matched by Viktor Hovland, Patrick Cantlay, Corey Conners and Brandt Snedeker.
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