Rudgeley, who hails from Perth in Western Australia, birdied three of the last four holes as she signed off with a six-under-par 66 on Troon Portland for a 12-under 204 total.
She finished a shot ahead of both overnight leader Darling (71) from Broomieknowe and England’s Emily Toy (69) in becoming the first Australian to land the title on the Ayrshire coast.
“It feels awesome,” said Rudgeley, who had already climbed to 166th in the World Amateur Golf Rankings on the back of three domestic victories this season.
“Getting an international win was definitely on my bucket list and to my name on such a great trophy means a lot.”
Helped by an eagle-3 at the ninth, Darling was still in with a chance of adding this title to her St Rule Trophy success in St Andrews last month before being scuppered by a bogey at the 16th.
“I knew I needed a low one and I was able to do it, so that’s great,” added Rudgeley of a bogey-free closing effort that contained six birdies.
“I drove the ball straight and holed a few good putts when I needed them. That’s what you have to do and that’s what got me over the line.
“Winning is always awesome but claiming an international victory means even more.”
Royal Troon’s Hazel MacGarvie finished fifth on eight-under, one ahead of Scottish champion and St Regulus member Chloe Goadby.