The former world number three was given a wildcard to the WTA Premier event in Miami, Florida, and despite not holding serve in the second set against Radwanska, Petrova responded in the third to beat the 23-year-old Pole in two hours and 34 minutes.
Having lost in the first round of the BNP Paribas Open and the Dubai Tennis Championships, Petrova won her first match in three tournaments, while it was also her first victory of 2014 outside of qualifying.
In the opening set, Radwanska led 3-1 before losing three of her next four service games as Petrova took the set 7-5.
The 31-year-old Russian barely got going in the second set, as Radwanska wrapped it up in just 29 minutes, but Petrova broke her Polish opponent on the first three opportunities in the third to build a 4-1 lead.
Ranked 205th in the world, Petrova battled on to triumph and set up a second-round clash with German 14th seed Sabine Lisicki.
Another wildcard, Rebecca Peterson of Sweden, also advanced after Germany's Mona Barthel withdrew with a stomach complaint when trailing by a set and 4-2.
But the other wildcards, Victoria Duval, Anett Kontaveit and Heather Watson were all eliminated, going down to Kiki Bertens, Madison Keys and Virginie Razzano respectively.
Croatian Donna Vekic, 17, struck a blow for her generation with a 7-6 (7-2) 6-2 win over fellow qualifier Japan's Kimiko Date-Krumm, 43.
After a tight first set, Vekic overran her Japanese opponent in the second, winning the last four games to prevail in one hour and 39 minutes.
Vekic will face Russian 28th seed Svetlana Kuznetsova in the next round.
Austria's Patrice Mayr-Achleitner overcame Karin Knapp of Italy 3-6 6-1 6-4 and American Coco Vandeweghe trumped Marina Erakovic of New Zealand 6-4 7-6 (8-6).
Czech Barbora Zahlavova-Strycova defeated Monica Niculescu of Romania 6-3 6-4 and Argentina's Paula Ormaechea stormed home against Pole Katarzyna Piter, winning 7-6 (7-0) 6-1.
Shuai Peng won 7-5 6-0 against Karolina Pliskova, Alison Riske fought back to triumph 1-6 7-5 6-2 against Nadiya Kichenok, Yvonne Meusburger dumped Lourdes Dominguez Lino 6-3 6-0, Andrea Petkovic edged out Maria-Teresa Torro-Flor 6-3 6-4 and Zarina Diyas eliminated Alexandra Cadantu 6-4 3-6 6-2.
Ajla Tomljanovic knocked off Kristina Mladenovic 7-6 (7-4) 6-4, Olga Govortsova won the battle of the qualifiers 2-6 6-0 6-3 over Shahar Peer, Christina McHale defeated Jie Zheng 6-4 6-2, Lauren Davis cruised past Shuai Zhang 6-2 6-3 and Vania King thrashed Estrella Cabeza Candela 6-0 6-0.