In a match which was stretched out over three days due to repeated rain delays, Stosur wound back the clock with a brutal display to take the fourth-round clash 7-6 (7-0) 6-3.
Having dispatched the past two beaten finalists, and in arguably the form of her career, Stosur will now face Bulgarian world No.102 Tsvetana Pironkova for a semi-final berth.
Pironkova came from a set and a break down to eliminate world No.2 Agnieszka Radwanska 2-6 6-3 6-3 and book her first French Open quarter-final.
Victory there would set up a semi-final showdown with either world No.108 Shelby Rogers or Spanish fourth seed Garbine Muguruza.
The stunning upset lands Stosur in her fourth quarter-final at Roland Garros, following a 2010 final appearance and semi-final runs in 2009 and 2012.
It is her first grand slam quarter-final appearance since the US Open in 2012.
And it was built on a blistering start overnight, Australian time, when Stosur took out her frustrations of a two-day rain delay on the world No.6.
In a 39-minute burst, before rain again halted play, Stosur wrested control of the match from her younger, more-fancied rival – coming back from a break down to take the first set before taking the advantage in the second.
Following a brisk hold of serve, Stosur pounced on Halep serve with crushing forehands to level the first set at 5-5.
In the tiebreak, she truly came alive, sweeping her more-fancied rival in devastating fashion to win it to love.
Halep struggled to cope with Stosur’s powerful groundstrokes and was routinely forced into error, while the Australian’s serve also caused the Romanian problems.
Stosur continued the onslaught into the second set, earning the crucial break in the opening match to have Halep – dubbed the tournament darkhorse by three-time champion Arancha Sanchez Vicario – well and truly on the back foot.
The pair traded service games – with Stosur saving two break points – before rain halted play with Stosur up 3-2 and about to serve.
After a further two-hour-and-forty-minute delay, Stosur picked up where she left to consolidate her break and take a 4-2 lead.
She had a chance to end the fight in her opponent, but was unable to convert on four break points in the next game – though a lucky bounce off the netcord let Halep escape with one point.
However, following a quick hold, Stosur put Halep under pressure once again – and again her rival cracked, sending the first of two match points long from a wild volley to hand Stosur her spot in the final eight.
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