Keys notched her 15th straight victory as she triumphed 4-6 7-6 (9-7) 6-3 on Wednesday (Thursday AEDT) to set up a clash with Swiss wildcard Belinda Bencic, who ousted third seed Coco Gauff.
Vekic, the Olympic silver medallist in Paris, put up a terrific defence in the first set, fending off three break points in the second game and another in the fourth, and dropped only three of her first-serve points.
She had a 5-3 head start in the tiebreak but Keys dug in her heels, clinching it with an unreturnable serve as the Croatian thrust her racquet to the court in frustration.
Keys took the momentum from there and she closed out the comeback win with one of her lethal forehands to wild cheers from the home fans.
The American joy was tempered earlier in the day, as Bencic pulled off an upset by beating Gauff 3-6 6-3 6-4, less than a year after giving birth.
In the tightly contested third set, it was Bencic who struck first as she came back from 0-40 down to break Gauff for a 5-4 lead, then closed out the victory on her first match point.
"Obviously, this is why you are practising and working hard all your life, so it's super nice to play in this kind of atmosphere," Bencic said.
"The way you cheered before the match ... I had chills and goosebumps and I kind of just put the serve into the court because I was so nervous."
Top seed and world No.1 Aryna Sabalenka easily dispatched British lucky loser Sonay Kartal 6-1 6-2.
In the quarter-finals Sabalenka, a two-time Australian Open champion, will meet 24th-seeded Russian Liudmila Samsonova, who crushed Italian sixth seed Jasmine Paolini 6-0 6-4.
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