Swiatek will face Madison Keys in Thursday's semi-final, after the 18th seed recovered from being bageled in the first set to beat Tunisian Ons Jabeur 0-6 7-5 6-1.
Swiatek, bidding for her third title this year, broke to lead 3-1 in the first set, but Haddad Maia bounced back to break twice, saving three break points in between to level at 4-4, and took the opening set.
That was the first set the Pole had dropped in the tournament, but she had an emphatic response, completing a bagel in the second set, winning two service games to love.
Swiatek, last year's losing finalist, continued in the same vein in the deciding set, winning four of the last five games.
Later on Tuesday Jabeur, the 2022 champion and eighth seed, appeared to be cruising towards an effortless win, taking the first set in only 24 minutes.
However, the American world No. 20 fought back and forced a decider where she broke twice to reach the semi-finals in Madrid for the first time.Â
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