Third seed Petkovic looked set for an early exit after losing the first set 6-1 to Chanelle Scheepers but she rebounded to win the next by the same scoreline before eventually coming through 1-6 6-1 6-2 against her South African opponent.
Fifth seed and Petkovic’s German compatriot Kerber also had to battle back from a set down but she defeated Russia’s Evgeniya Rodina 3-6 6-3 6-4.
Jankovic, seeded sixth, appeared set for a rather more routine win but the Serbian also went the distance before seeing off Germany’s Tatjana Maria 6-3 6-7 (6/8) 6-1, while French eighth seed Garcia was taken to a decider before claiming a 6-3 4-6 6-3 win over American wildcard Sachia Vickery.
Ninth seed Samantha Stosur enjoyed a rather more comfortable day as she progressed into the second round, with the Australian defeating Bulgarian qualifier Sesil Karatantcheva 6-2 6-4, while Switzerland’s Belinda Bencic, seeded 12th, hammered Casey Dellacqua 6-1 6-2.
It was not all plain sailing for the seeds though as Varvara Lepchenko of the United States and Russia’s Anastasia Pavlyuchenkova both exited at the first hurdle.
Tenth seed Lepchenko was trailing 6-2 2-1 to Romania’s Andreea Mitu before retiring, while Pavlyuchenkova, seeded 14th, was losing 6-4 3-0 to Spanish qualifier Sara Sorribes Tormo before she, too, retired.
There were also first round wins for Sloane Stephens, Jana Cepelova, Madison Brengle and Lara Arruabarrena, while Czech qualifier Lucie Hradecka defeated Kristina Kucova 7-5 6-3 to progress to the third round.