Garbin reached the semi-finals of this event last year only to withdraw with breathing difficulties when leading Martina Hingis 4-3 in the first set.
But she had no such problem against Petrova as she chased down almost every shot and used her court coverage to overcome the powerful Russian.
It was her first win over Petrova in five encounters.
"I feel like I didn't finish the tournament last year," Garbin said.
"To come back here and win this first round match was very tough because Nadia is one of the best players in the world. I'm proud of myself today."
After two hard-fought sets, Garbin looked to be cruising to victory when she led 5-0 in the decider, but she began to suffer from nerves and allowed Petrova to claw her way back to 3-5.
But the Italian regained her composure and when the powerful Russian hit a forehand into the net, Garbin was through to the second round.
"The key was to give her back every ball," Garbin said. "I ran so much today -- three hours almost -- I ran for everything."
Eighth-seeded Hungarian Agnes Szavay was also a first-round loser, bowing out to qualifying "lucky loser" Yuliana Fedak of Ukraine.
Fedak only made the main draw when countrywoman Julia Vakulenko withdrew injured at the last minute, but came back from losing the first set to win 3-6, 7-5, 6-2.
Defending champion and third seed Dinara Safina of Russia struggled past Australian-based Slovakian Jarmila Gajdosova 4-6, 6-1, 6-2.
In other matches played on a rain-affected second day, fourth seed Patty Schnyder of Switzerland cruised past Russian qualifier Alisa Kleybanova 6-1, 6-3 and two-time Grand Slam winner Amelie Mauresmo crushed Ukraine's Olga Savchuk 6-1, 6-1 in a little under an hour.
Mauresmo now plays compatriot Nathalie Dechy in the second round.
In a late match, Italian Francesca Schiavone unexpectedly progressed to the second round when Meghann Shaughnessy was forced to withdraw despite the American leading 6-0, 1-0 at the time.