Glushko, ranked 98 in the world, won the first set against the 21st seed, though Flipkins levelled the match up at 1-1 by taking the second set 6-3.
The third and final set proved to be a topsy-turvy affair, with the Israeli at one point finding herself 3-1 up on her serve. However, the Belgian battled back, breaking serve twice to take a 4-3 lead, but that only served to drive Glushko up to another gear. Breaking serve immediately to level the set up at 4-4, she then held her serve, before breaking again, taking the match on her first match point.
Awaiting her in the third round will be either German Dinah Pfizenmaier or the tenth seed, Italian Sara Errani.
Elsewhere, Shahar Peer’s miserbale week in Paris is over after she lost her first round women’s doubles match. Alongside Daniela Hantuchova, they were beaten 6-3, 6-3 by the fifth seeds Cara Black and Sania Mirza.
Israel’s other representative is Jonathan Erlich, who along with Brazilian Marcelo Melo, also won on Thursday as they beat the sixth seeds, Indian Rohan Bopanna and Pakistan’s Aisam-Ul-Haq Qureshi, 6-3, 6-4. They next take on Czech Frantisek Cermak and Russian Mikhail Elgin.