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The US Open champion lost six games in a row to surrender the first set before reeling off six on the spin to take the match into a decider but never looked comfortable and failed to claw back a 3-0 deficit despite saving two match points.
Of the four Australian men and five women to start in the main singles draws, Stosur was the only player to win a match - although her defeat was hardly a surprise give her poor record on grass. Stosur saved two match points trailing 5-3, one of them with a sensational winner to end a fierce baseline rally, and looked poised to level at 5-5 as she led 40-15 on serve but crumbled, slicing a backhand into the bottom of the net to hand the 72nd-ranked Rus victory.
"I'm very happy with this win today, especially on the grass, as I haven't won a match in the main draw before," said Rus.
"It was very nice to play on Court One. I hope to play the same again in the next round also and we will see what happens."
