The US Open champion, who will face Italian Sara Errani, a 6-3 7-6 winner over German 10th seed Angelique Kerber, for a place in Saturday's final, advanced into the last four without dropping a set.
Stosur, who reached the semi-finals in 2009 and the final in 2010 in the clay court grand slam, prevailed on composure and tactical finesse, using her kick-serve to stave off nine of 10 break points.
She struggled at first with her opponent's power but Cibulkova collapsed after losing the opening set, with Stosur winning six games in succession to wrap it up after 85 minutes.
Stosur will start as favourite against 21st seed Errani, who had never beaten a top 10 players in 28 attempts before knocking out world number 10 Kerber.
But Stosur was reluctant to forecast the outcome: "It can be a great day or a bad day."
A dejected Cibulkova conceded there was not much she could do.
She said: "She's putting the ball so high. Her kick-serve gets me out of the court so much that I cannot do anything. So if I want to go against the serve I go here, and if I want to go back I'm like three metres behind the baseline."
Stosur broke twice in the opening set and definitely stamped her authority on the contest when she saw off two break points in a hard-fought seventh game.
She used her kick-serve to pull her opponent off the court, opening it up for a forehand winner as she claimed the first set after 54 minutes.
The same trick worked again in the second game of the second set, with Stosur saving another three break points en route to a straightforward victory.