Mladenovic rallied for a 2-6, 6-3, 6-3 victory against the Wimbledon semifinalist. She will face American qualifier Taylor Townsend in the second round.
On the men's side, Americans Jack Sock, Sam Querrey and Steve Johnson each advanced with straight-sets victories. Other first-round winners included the Dominican Republic's Victor Estrella Burgos and Dudi Sela of Israel.
Seventh-seeded Kevin Anderson of South Africa and No. 11 seed Denis Istomin of Uzbekistan reached the third round with straight-sets victories. Anderson defeated Russia's Evgeny Donskoy 6-3, 6-4, and Istomin eliminated Australia's Bernard Tomic 6-4, 7-6 (6).
Sock beat Michael Berrer of Germany 7-6 (2), 6-4. He grabbed control by breaking Berrer in the first game of the second set.
Next up for Sock is a Wednesday match against No. 2 seed Milos Raonic, who had a bye in the first round.
There will be a new titlist in the women's tournament after No. 2 seed Ekaterina Makarova of Russia cruised to a 6-1, 6-1 victory against two-time defending champion Magdalena Rybarikova of Slovakia. Rybarikova had won her previous 10 matches in the tournament.
Christina McHale upset fourth-seeded Sloane Stephens 6-4, 4-6, 6-0 in an opening-round match on a side court that drew a standing-room-only crowd to go along with fans lined up outside a perimeter fence.
It was the first meeting on the WTA tour between the two Americans, although there was a level of familiarity.
"Obviously playing someone I've grown up with and played against a lot, that's tough playing someone like that," said Stephens, 21.
McHale, 22, will play another American -- Vania King -- in the second round.
"I don't think Sloane played her best in the third set so I just stayed focused," McHale said.