Kim Clijsters of Belgium challenges a line call during her match against Iveta Benesova of Czech Republic at the Brisbane International tennis tournament Jan 5, 2012.
Benesova had beaten top seed Stosur in the second round on Wednesday and was targeting the Australian Open champion in their quarter-final to achieve a special double of beating grand slam champions on successive days.
The 28-year-old Belgian refused to let that happen by racing to a 5-1 lead in the first set and then, after tightening up a little to allow the Czech to narrow the gap, serving out 6-3.
Clisjters made short work of the second set, with Benesova holding her first service game before the four-times grand slam champion raced through winning the next five games to again have a 5-1 lead.
Bensova finally held her serve again in the seventh game but it only delayed the inevitable and Clijsters served out in just under 80 minutes.
Andrea Petkovic of Germany hits a return to Kaia Kanepi of Estonia during their match at the Brisbane International tennis tournament, Jan 5, 2012.
Estonia's Kaia Kanepi earlier provided the upset of the quarter-finals when she beat second seed and world number 10 Andrea Petkovic 6-1 7-6.
The hard-hitting Kanepi had been cruising to victory but needed five match points to seal the win as her German opponent offered some late resistance.
Petkovic had been hampered by a back injury throughout the match but was able to increase the pressure when the 26-year-old was serving for the match at 5-4 and eventually forced a tie-break.
Despite having an opportunity to finish off the match on three further occasions, Kanepi finally managed to seal the win 9-7 in the tie-break after one hour, 40 minutes to set up a semi-final against Francesca Schiavone.
Third seed Schiavone had earlier ground down former world number one Jelena Jankovic 5-7 7-6 6-3 in a drawn-out quarter-final that lasted almost three hours as both players squandered numerous match point opportunities.
Jankovic wasted two match points in the second set while 2010 French Open champion Schiavone also squandered two match points of her own in the third.
Slovakia's Daniela Hantuchova had a walkover into the semi-finals after Serena Williams withdrew on Wednesday with an ankle injury that she sustained in her second round victory over Serbia's Bojana Jovanovski.
Kaia Kanepi of Estonia reacts after winning her match against Andrea Petkovic of Germany at the Brisbane International tennis tournament, Jan 5, 2012.
In the men's draw, second seed Gilles Simon started sluggishly but managed to overcome Santiago Giraldo 7-6 6-4 in the quarter-finals.
Simon, who beat American Ryan Sweeting and Australia's James Duckworth in the first two rounds, is building nicely for the Australian Open later this month in Melbourne, something the Frenchman was pleased with.
"I've already played three good matches so it's good preparation for Melbourne," Simon said.
"I'm feeling good, I'm moving better and better everyday."