The 26-year-old, who is ranked world No. 45 by the Women's Tennis Association (WTA), outlasted Nadia Podoroska of Argentina 6-4, 4-6, 6-4 in the first round on Wednesday.
Up next for the Polish player at the hard-court tournament in Monterrey is Israel's Lina Glushko.
The Monterrey Open, which runs until Saturday, is the final warm-up for the Pole before the US Open Grand Slam event in New York.
Fręch last month reached the final of the Prague Open clay-court tournament in the Czech Republic, where she was overpowered by countrywoman Magda Linette.
The championship match in Prague marked Fręch's maiden WTA singles final.
The 2024 US Open begins on Monday, August 26.
(gs)
Source: IAR, PAP