The Pole and the American beat Hayley Carter of the United States and Brazil's Luisa Stefani, 2-6, 6-3, 10-6, in their round-of-32 clash on Friday.
The Polish 19-year-old and her US doubles partner will now take on the winners of a match pitting Russians Elena Vesnina and Vera Zvonareva against the Czech Republic's Lucie Hradecká and Germany's Laura Siegemund.
Poland’s Świątek on Thursday cruised into the second round of the Madrid Open women's singles, with a 6-1, 6-1 win over American Alison Riske.
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Source: PAP