Williams sent defending champion Petra Kvitova packing in one of the most eagerly-anticipated matches of the tournament so far before second seed Azarenka dispatched Austrian Tamira Paszek in straight sets.
Four-time champion Williams turned on the style on her debut under the roof to out-muscle her Czech opponent in a 6-3 7-5 win.
"I had a good talk with my dad, he motivated me, and my sister as well," she said.
"I just took to heart what everyone said. I really prayed about it, just to have calmness of mind and just go forward and do the best I can do, whether that's winning or losing."
Meanwhile, Azarenka saw off Paszek thanks to a tie break in the second set after the Austrian fired long on match point to win 6-3, 7-6 (7/4).
Eighth seed Angelique Kerber booked her place in the last four with a hard-fought win over fellow German Sabine Lisicki.
The German claimed a 6-3, 6-7 (9/7), 7-5 win over Maria Sharapova's conqueror after two-and-a-half hours to reach her first Wimbledon semi.
And Agnieszka Radwanska claimed the final semi-final spot after another late night finish under the roof.
She defeated Maria Kirilenko 7-5, 4-6, 7-5 following the tie being moved to Centre Court.
