A two-hour fog delay kept the field waiting on Thursday before Scott ground out a first-round three-over-par 73 playing his milestone 100th consecutive major championship.
American Sam Stevens snared the clubhouse lead with a two-under 68 as once again the world's best players battled hard to deal with one of the sternest tests in golf.
Two birdies in his first three holes helped world No.2 Rory McIlroy take the early lead before the back-to-back Masters champion signed for a 69 to sit ominously one shot off the pace after the morning wave.
Starting at the 10th, McIlroy holed a 10-foot putt at the short but perilous 11th and then followed that up, holing from more than twice that distance at the long 12th.
He slipped back to level par with bogeys on 13 and 16 before surging with his third birdie of the day on the par-4 third, then making a magical eagle three on No.5.
McIlroy soured his round with successive bogeys to finish but still wound up in red numbers alongside his Swedish playing partner Ludvig Aberg as wind speeds of almost 50kph - and forecast to become much worse in the afternoon - challenged the field.
Earlier, play was suspended for two hours after just 30 minutes of action as the fog encircling the Long Island venue worsened to such an extent that players on the 12th tee in particular could not even see the landing area on the fairway.
The 126th US Open is back at Shinnecock Hills for a sixth time, with only three players out of 654 having ever posted sub-par scores for the championship.
Players were initially held on the course for 30 minutes before a decision was taken to recall them on Thursday (Friday AEST).
When play resumed at 9.05am local time, the wind had already picked up to make conditions even more treacherous.
Scott wobbled with a double-bogey six at the 16th hole but struck straight back with a birdie on 17 to stay within touch of leader Stevens.
Of the other Australians out in the morning, Lucas Herbert carded a four-over 74 and his LIV Golf Ripper GC captain Cameron Smith a 75.
Smith's round was blighted by a dreaded triple-bogey six at the par-3 seventh hole, when the former British Open champion needed two shots from a bunker and then three-putted.
Min Woo Lee had an afternoon tee slot.
Former world No.1 Jason Day's tournament lasted only nine holes before he withdrew with a back injury.
A grimacing Day bogeyed seven holes to turn in 42 before the 2011 runner-up calling for officials and was carted back to the clubhouse for treatment.
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