Svitolina said on Monday she would not play against players from Russian or Belarus -- unless they were competing under a neutral banner -- as a protest against Russia's invastion of her homeland.
However the prospect of Svitolina boycotting her first round game was erased earlier Tuesday when the ATP and WTA issued a statement effectively granting her wish.
That left world number 15 Svitolina free to swat aside 20-year-old Potapova, ranked 81 in the world, with ease in a 6-2, 6-1 win.
Svitolina, who played in a yellow top and blue skirt, the colors of the Ukranian flag, thumped her chest repeatedly after wrapping up the win before shaking hands with Potapova.
"It's a very special atmosphere each time I play here, and especially today, it's a very special match and moment for me," Svitolina said.
"I'm in a very sad mood, but I'm happy that I'm here playing tennis."
"I was just focused from the beginning. I was on a mission for my country."
Svitolina is donating the entirety of her earnings in Monterrey to the Ukrainian military.
"It's a very special event, all the prize money I earn here is going to the Ukrainian army, so thank you so much for the support," she said.