Stosur was beaten 7-5 7-6 (6-0) by Tsvetana Pironkova, and has failed to register a win on the grass surface in over a year.
Stosur was joined by fellow Aussies Casey Dellacqua and Jarmila Gajdosova who were also defeated, leaving young gun Daria Gavrilova as Australia's only remaining hope in the tournament.
Lucie Safarova's Aegon International campaign was ended by Dominika Cibulkova, while Caroline Wozniacki battled through to round three.
Dominika Cibulkova dumped third seed Lucie Safarova out of the Aegon International, but Caroline Wozniacki kept her campaign going with a dogged display against Gajdosova.
Melbourne (Australia) Age - Tennis: Eastbourne International: Samantha Stosur, Casey Dellacqua and Jarmila Gajdosova lose in first round
— Tennis Headlines (@1stTennisNews) June 23, 2015
Safarova, beaten in this month's French Open final by Serena Williams, enjoyed a run to the semi-final of Wimbledon last year, but failed to find form on the grass at Eastbourne - losing 7-6 (9-7) 6-4.
The first-set tie-breaker had much in common with Wozniacki's, with the second-seeded Dane prevailing 7-6 (7-4) 6-2 in her match.
Both involved a flurry of points against the serve as returning appeared to provide the greater advantage.
While Wozniacki was able to triumph and emerge stronger for it, Safarova's challenge faded, with a solitary break in the first game of the second set ultimately decisive.
Madison Keys served up a meek defence of her title, losing 6-2 6-2 to Belinda Bencic, while Agnieszka Radwanska enjoyed a 6-0 6-2 rout of Irina Falconi.
Canada's Eugenie Bouchard, who rose to prominence with last year's run to the All England Club final, was taken to a first-set tie-break, but proved strong for Alison Riske in a 7-6 (7-5) 6-3 win.
With Aegon Classic champion and 2014 beaten finalist Angelique Kerber withdrawing through illness, Coco Vandeweghe received a free pass to round three.
Ekaterina Makarova was a major casualty as the fourth seed fell in straight sets to Johanna Konta, with the Australian-born British player a popular 6-2 6-4 winner.
Another seeded player to be dumped out was Carla Suarez Navarro, beaten 6-1 7-5 by Sloane Stephens.
In other matches, Garbine Muguruza overcame Polona Hercog 5-7 6-3 6-0, while Sara Errani, Svetlana Kuznetsova, Heather Watson and Daria Gavrilova all progressed.