The Briton, who turned 28 on Friday, followed up on a Thursday double-header, where she beat Sloane Stephens and then Venus Williams, by overcoming Vondrousova 6-3 3-6 6-1.
Konta broke Vondrousova twice in the opening set, but the Czech bounced back with two breaks of her own to level up at one-set all.
But it was Konta who blitzed the decider, breaking three times to set up a last-four meeting with Kiki Bertens, the benefactor of Naomi Osaka’s withdrawal before their quarter-final.
The other semi-final will see Karolina Pliskova take on Maria Sakkari.
Pliskova recovered from a set down to beat Victoria Azarenka 6-7(5) 6-2 6-2 earlier on Friday, while Sakkari bounced back to beat Kristina Mladenovic 5-7 6-3 6-0.