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-set victories. Other first-round winners included 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-set 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.
Querrey beat countryman Michael Russell 6-4, 6-3, and Johnson eliminated Australia's James Duckworth with a 6-3, 7-6 (4) win.
Fourteenth-seeded Leyton Hewitt defeated fellow Australian Marinko Matosevic 6-4, 6-3 to advance to the third round where the 2004 champion will meet the winner of the Sock-Raonic match.
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 Magadalena Rybarikova of Slovakia. Rybarikova had won her last 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.
The 22-year-old McHale 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.
No. 5 seed Anastasia Pavlyuchenkova moved into the second round with a 6-2, 6-2 win over France's Virginie Razzano. Pavlyuchenkova next faces Japanese qualifier Hiroko Kuwata.