Cibulkova, beaten in last year’s final by Li Na, weathered the inevitable comeback by the Belarusian blaster and ran her ragged in a match of the highest quality to earn the 6-2 3-6 6-3 win.
The pint-sized 25-year-old blasted 44 winners and broke Azarenka twice in the deciding set, sealing it when her opponent netted after two hours and 10 minutes.
Cibulkova will play the winner of Serena Williams and Garbine Muguruza for a place in the semi-finals.
“Today was extremely, extremely good match from my side. I would say it was a high level of tennis,” said Cibulkova.
“The first set, the way I played, was just really, really – no mistakes. I was going for my shots and I was just doing the right things.”
“I was really putting her under so much pressure. The tennis she’s playing goes well with my tennis.
“But today I would say it was the best match we ever played. I lost to her a few times before that I was a set up and maybe 5-2 or 5-3 up in the second set and I didn’t manage to finish it…
“Today I was not thinking about the score, I was just going for it. When I was up I was going for it even more.”