The Australian Open champion Azarenka, playing in her first tournament as world No. 1, handled Belgian Yanina Wickmayer 6-0, 6-4 in 67 minutes on the hardcourts at Khalifa International Tennis Complex.
The 22-year-old Belarusian Azarenka is now a sizzling 15-0 this season, which also includes a title in Sydney last month. She'll face fourth-seeded Pole Agnieszka Radwanska in Saturday's semifinals.
Meanwhile, the third-seeded Stosur held off Romanian Monica Niculescu 6-2, 2-6, 6-3 on Day 5. The Aussie Stosur popped seven aces in the 1-hour, 44- minute affair to reach her first semifinal of the year.
"It's a really good feeling," Stosur said.
Up next for Stosur will be fifth-seeded French slugger Marion Bartoli, who held off Czech left-hander Lucie Safarova, 7-5, 4-6, 6-1. The former Wimbledon runner-up Bartoli is 3-2 lifetime against Stosur.
The steady Radwanska, quietly up to No. 6 in the world, routed 19-year-old American Christina McHale 6-1, 6-1 in a mere 61 minutes.
Radwanska will now face Azarenka for an 11th time, with the top-ranked Belarusian holding a commanding 7-3 lead in their lifetime series, including a victory in last month's Aussie Open quarterfinals.
The 2012 Doha champion will earn $385,000.