Cibulkova, ranked 16th in the world, must have been fearing the worst when she was broken in the first game of the match, but the Slovakian responded immediately, breaking back in the very next game.
Cibulkova broke again in the sixth game of the set, before holding serve and winning against the serve for a third time to secure the first set 6-2.
Azarenka looked to respond, and once again broke her opponent in the first game of the set. She held her serve for the next game before losing four in a row to give Cibulkova the advantage.
The world number one fought back and had a chance to serve for the set, but she was broken once again by Cibulkova to make it 6-6.
The 23-year-old went on to win the tie-break 7-4 to seal a famous victory.