Number one seed Konta broke Barty’s second service game to take an early advantage in the first set, holding on to consolidate.
The Brit looked strong, and came close to breaking again, but Barty – ranked 88th in the world - defended four break points to prevent Konta from widening the gap.
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As it looked like Konta might have to wrap up the first set the hard way, she fought back to break once more and take the first set 6-3.
Australian Barty fought back in the second set, catching Konta out on a second break point to take a 3-2 advantage, but Konta broke back not long afterwards with an audacious lob to level at 4-4.
After holding her next serve Konta looked determined to finish the job, taking a 30-15 lead in what ought to have been the final game of the second set, before Barty found a way back in with some well-placed returns.
Barty started to show the strain at 6-5 in the second set as she fluffed her lines to give Konta match point. Though Konta failed to make the conversion, the result seemed a foregone conclusion as Barty quickly gave Konta the advantage once more, which she duly made the most of.
The British number one will face Croatia's Donna Vekic in the semi-final after she beat Greece's Maria Sakkari 6-2 6-3 later on Friday.
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