Australian spearheads Samantha Stosur and Bernard Tomic have safely progressed to the second round of the French Open in Paris.

Riding high after claiming her first title of the year in Strasbourg at the weekend, Stosur downed rising American Madison Brengle 6-1 6-3 before Tomic dug in for an impressive 6-3 3-6 6-3 6-4 victory over Italian qualifier Luca Vanni.

Stosur’s victory thrust the women’s 26th seed and former finalist into a meeting on Wednesday with French wildcard Amandine Hesse, who earlier eliminated Jarmila Gajdosova in three sets.

Seeded 27th in the men’s event, Tomic could face Davis Cup teammate Thanasi Kokkinakis next after grinding out just his second win in six trips to Paris – and first since 2012.

Vanni had beaten Tomic in a tough three-setter at altitude in Madrid earlier this month and threatened to get the better of him once again on Monday.

Tomic, though, hung tough and snared the decisive break in the fourth game of the pivotal third set to take control.

He broke the Italian again early in the fourth before serving out the match after two and 32 minutes.

Ajla Tomljanovic was the first Australian through to round two storming past compatriot Casey Dellacqua 6-2 6-2 in just 62 minutes.

The 22-year-old world No.58 struck 29 winners to Dellacqua’s seven to progress to a second-round showdown on Wednesday with German 11th seed Angelique Kerber.

“Casey’s a very tricky player and we’ve had some tough matches in the past so I was ready to battle today,” Tomljanovic said.

“Even if the scoreline says it was easy, it really didn’t go that way.

“I had to stay focused from the beginning and I’m very happy with this and the way I performed today.”

Coached in tandem by Samantha Stosur’s mentor David Taylor, Tomljanovic upset former world No.2 Agnieszka Radwanska en route to the last 16 in Paris last year and looms as a dark horse to make another strong run in 2015.

Like Dellacqua, Gajdosova and fellow Australian Sam Groth crashed out of the claycourt major on day two.

Gajdosova suffered a disappointing 2-6 6-3 6-2 loss to French wildcard Amandine Hesse, while her ex-husband Groth was gallant in a 6-7 (5-7) 6-3 6-3 6-3 loss to accomplished 21st seed Pablo Cuevas.

Ranked 272nd in the world, Hesse had never previously won a grand slam match before.

After taking the opening set, Gajdosova’s game dropped off as the local hope raised hers to thrill a partisan French crowd on Court 3.