The Polish world No. 1 saw off France's Russian-born Varvara Gracheva 6-0, 6-7, 6-2 in the second round of the women’s singles on Wednesday night.
The top-seeded Polish player, who had a bye in the first round, will now face Marta Kostyuk of Ukraine for a place in the quarterfinals.
The Cincinnati Open hard-court tournament is for many top tennis players the final warm-up before the US Open.
Earlier this month, Świątek claimed bronze in the women's singles competition at the Paris Olympics after defeating Anna Schmiedlová of Slovakia in the third-place match.
In June, the 23-year-old Pole won the French Open Grand Slam tournament in Paris for the fourth time.
(gs)
Source: IAR, PAP