North Berwick, 15, Crawford beat Sweden’s Kajsa Arwefjalli 2&1 in their first round match in the top half of the draw at the Norfolk venue.
It came after Chloe Goadby, the 2021 Scottish champion, fell at the opening hurdle to Italy’s Anna Zanusso in a 5&4 defeat.
Playing in one of the final matches, Darling found herself up against England’s Isabelle Simpson after 12 holes before winning the next two to turn the tide.
The Broomieknowe player went on to win 2&1 and now meets Germany’s Viktoria Maria Hund in the second round on Thursday morning.
“Yeah, it was a hectic round with a few things happening here and there which was almost hard to deal with at times,” admitted Darling, the current R&A Girls champion, of her hard-fought victory.
“But, when you’re down, you know you can get something out of the bag. So luckily a few putts fell towards the end.
Crawford, the R&A Girls Under-16 amateur champion, will face Minchinhampton-based Welsh player Ffion Tynan in the next round.
“Making a top-64 finish was my first target and anything beyond that is just a bonus,” admitted Crawford, who also won the Scottish Women’s Open Helen Holm earlier in the year.
On a day when Japan’s top qualifier Ami Yamashita pulled out, Darling and Crawford were among just eight players from Britain and Ireland to keep their hopes alive.
In the professional ranks, Scotland’s No. 1 Gemma Dryburgh will play for a bargain price of $9 million in the KPMG PGA Championship, which kicks off in Congress on Thursday.
It follows that the purse for the women’s third major of the season has been doubled – the top prize of $1.35 million has been increased by the same ratio – in another welcome boost for Dryburgh.
On the men’s side, Bob MacIntyre is among the Scots taking part in this week’s DP World Tour event, the BMW International Open in Munich, while 2014 winner Colin Montgomerie rides the saltire at the US Senior Open at the Saucon Valley Country Club in Bethlehem, Pennsylvania.
Former winner Sandy Lyle tries to qualify for the 150th Open at 64