North Berwick 15-year-old Crawford beat Swede Kajsa Arwefjalli 2&1 in her first-round match in the top half of the draw at the Norfolk venue.
That came after Chloe Goadby, the 2021 Scottish champion, had fallen at the opening hurdle to Italian Anna Zanusso in a 5&4 defeat.
Playing in one of the later matches, Darling found herself one down to England’s Isabelle Simpson after 12 holes before winning the next two to turn the tide her way.
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 an eventful round with a few things happening here and there, which was almost hard to kind of cope with at times,” admitted Darling, the current R&A Girls’ champion, of her hard-fought win.
“But, when you're down, you know you can pull something out of the bag. So, thankfully, a few putts dropped towards the end.”
Crawford, the R&A Girls Under-16 Amateur champion, takes on Minchinhampton-based Welsh player Ffion Tynan in the next round.
“Getting through to the top 64 was my first goal and anything past that is just a bonus,” admitted Crawford, who also won the Helen Holm Scottish Women’s Open earlier in the year.
On a day when leading qualifier Ami Yamashita from Japan bowed out, Darling and Crawford were among just eight players from Great Britain & Ireland to keep their hopes alive.
In the pro ranks, Scottish No 1 Gemma Dryburgh will be playing for a bumper $9 million prize pot in the KPMG PGA Championship, which starts at Congressional on Thursday.
It follows the purse for the third women’s major of the season being doubled - the first prize of $1.35m has been increased by the same ratio - in another welcome boost for the likes of Dryburgh.
In the men’s game, Bob MacIntyre is among the Scots teeing up in this week’s DP World Tour event, the BMW International Open in Munich, while 2014 winner Colin Montgomerie is flying the Saltire in the US Senior Open at Saucon Valley Country Club in Bethlehem, Pennsylvania.