Promising talents Alja Tomljanovic, Thanasi Kokkinakis and Daria Gavrilova also advanced with Sam Groth, Marinko Matosevic and Jarmila Gajdosova the Aussies to depart.
Tomic's victory was perhaps the most impressive as the 27th seed battled a virus while defeating italy's Luca Vanni 6-3 3-6 6-3 6-4.
After questionable form at the French Open in past years, Tomic's gutsy performance is rewarded with a second-round match against Kokkinakis - who overcame Georgia's Nikoloz Basilashvili 3-6 6-4 7-6 (7-4) 6-2.
“It’s always good to win my first main draw French Open,” he said.
“It’s great to be in the main draw this year and get a win. It was a scrappy win, but happy I got through in the end.”
29th-seed Kyrgios is on track to meet Andy Murray in the third round after thrashing Ukbekistan's Denis Istomin 6-3 6-4 6-3 - with the 20-year-old appearing to be untroubled by an elbow injury suffered in a Roland Garros lead-up tournament.
Continuing her good form after winning at Strasbourg at the weekend, Stosur blitzed American Madison Brengle 6-1 6-3.
The number 26 seed's preparation for Roland Garros was rushed because of her latest WTA title but Stosur believes she will settle quickly after her opening-round victory.
“I wasn’t planning on doing it, but then I did and winning the tournament overrides every thing else that you might be feeling," Stosur said.
“You feel like everything has been kind of a whirlwind but I have got tomorrow to feel a bit more settled and then keep going.”
Tomljanovic set up a meeting with Germany's 11th seed Angelique Kerber after overwhelming compatriot Casey Dellacqua 6-2 6-2.
21-year-old Gavrilova earned her first Grand Slam win with a straight sets victory over Sweden's Johanna Larsson 6-1 7-6 (7-3).
Wimbledon finalist Sabine Lisicki is awaiting Gavrilova in the second round.
“That’s my first grand slam win so I’m very happy,” Gavrilova said.
“It’s a great opportunity to play Lisicki ... she’s the type of player when she’s on that she can kill you.”