Last year's runner-up Stosur was in impressive form against Benesova and won through in just 68 minutes - 6-2 6-3.
The 27-year-old Australian will now face Simona Halep of Romania in the second round after Halep powered past Russia's Alla Kudryavtseva for the loss of just three games 6-2 6-1.
"It was nice to get back out there again and play a really solid first round," said Stosur after the match. "I thought I played really quite well today. I served quite well.
"The conditions weren't always easy with some gusts of wind. I'm very happy."
Former world number one Jelena Jankovic is also though to the second round after a routine victory over Ukrainian Alona Bondarenko 6-3 6-1.
Other winners so far on day one include 32nd seed Tsvetana Pironkova of Bulgaria and Gisela Dulko of Argentina.
Israel's Shahar Peer was a seeded casualty, with Spaniard Maria Jose Martinez Sanchez defeating the 19th seed 7-6 (7-4) 6-1.
Former top 10 player Jelena Dokic of Australia is also out after losing a topsy-turvy contest against Vera Dushevina of Russia. Dushevina won through 4-6 6-3 6-2.
























