The 17-year-old Broomieknowe player survived being one down playing the last to beat England’s Hannah Screen at the 22nd hole in a ding-dong last-16 clash on the Ayrshire coast.
Darling, the world No 48, having made a big jump on the back of her recent St Rule Trophy triumph in St Andrews, now meets 42nd-ranked Annabell Fuller after she defeated Maggie Whitehead 2&1 in an all-English encounter.
“I’m definitely tired, but my coach (Ian Muir) text me last night after a few gruelling weeks of golf and he told me ‘tiredness is a mentality’,” said Darling, who was taken to the final hole by fellow Scot Rachel Foster in her morning match.
“I kept reminding myself of that every time I felt a little bit tired. I thought ‘no I’m not tired, come on let’s do this’. It really paid off towards the end.
“I honestly can’t remember (playing that many holes in one day), but I’ve worked hard and this is what it takes.”
Darling, the 2018 R&A Girls’ Under-16 Open winner, added: “Hannah (Screen) is a great player and she really proved it when it came down to it. It was a great match.
“I had a few chances on the first and second extra holes but she proved what a great player she was. I’m obviously delighted to come out victorious on the fourth extra hole.”
Aboyne’s McWilliam, another member of the Great Britain & Ireland Curtis Cup squad, beat England’s Harriet Lynch by one hole, setting up her success by winning the 11th with birdie and 12th with par, and now meets Gracie Mayo from Wales.
Maintaining the form that enabled her to be the leading qualifier in last week’s Scottish Women’s Championship at Gullane, West Kilbride player Duncan recorded the biggest third-round win as she crushed Sara Byrne from Ireland 6&4.
Duncan, who was three up after four, takes on Jessica Baker from England as the tartan trio bid to land a first Scottish success in the event since Alison Rose landed the title at Cruden Bay in 1997.