The world number 50 needed less than 80 minutes to overcome her opponent 6-2 6-2 and reach the first Grand Slam semi-final of her career.
Vesnina immediately put Cibulkova under pressure in the opening game of the contest, with the Slovakian being forced to save three break points to hold her own serve.
It proved to be a sign of things to come, and Vesnina quickly rattled off five games in a row to move in control of the set before serving it out inside 40 minutes.
There was more of the same in the second set too as the Russian raced into a 4-0 lead before Cibulkova saved two more break points to finally get on the board.
A second hold followed, but Vesnina had not been forced to face a single break point on her own serve throughout and she continued that dominance by seeing out the match to love and booking her semi-final spot.