Both players struggled to hold serve throughout - there were 10 breaks during the match - as the Belarus player registered a narrow 6-4 7-5 win.
Azarenka, who lost to Venus Wiilliams in the third round at Beijing 2008 four years ago, is refusing to get carried away with her success despite being just one victory away from her first Olympic medal.
'It (winning a medal) still seems really far away,' Azarenka said. 'I'm not thinking about it at the moment. I'm just focused on myself and hopefully the result will take care of itself.
'I just have to stay focused now. It was definitely a really tough match today.
'We showed very high quality tennis and a lot of fight.'
She will now face Serena Williams in the semi-finals after the Wimbledon champion dashed Caroline Wozniacki's hopes.
Williams had not lost a set going into today's clash against Wozniacki, and the American looked in supreme form again, beating the former world number one in the first set before wrapping up a 6-0 6-3 win.