The British No.1 went a break up in the final set of a roller-coaster match and then had a break point at 4-4 to serve for the biggest win of her career.
But the five-time Grand Slam champion fought back to win 6-7 6-1 6-4 to send Poland through to the semi-finals and knock Great Britain out.
"I am just exhausted," said Swiatek. "The match was crazy, like so many changes of momentum. I thought I had it under control in the first set, but I got tight and I didn't want to make the same mistakes in the third.
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