Though she was the underdog in terms of ranking, Stosur has always thrived against Cibulkova - she won all three of their previous meetings in straight sets - and after an early 3-0 deficit she out-served, out-rallied and completely outplayed the Slovak, reeling off 12 of the next 13 games to prevail.
From 4-all in the first set Stosur won eight games in a row to close it out in straights.
"After a few games I was really able to settle down, dictating play and getting into the match, and once I got a lead it got easier," Stosur said afterwards. "It was good to turn it around from such a deficit.
"In a tournament like this you can get some really tough first rounds and today was one of those."
Stosur's win over the World No.10 was her first Top 10 win since beating then-World No.3 Victoria Azarenka in the final of Carlsbad last August. Stosur has been as high as No.4 in the world herself.
The 2011 US Open winner was asked about what's clicking for her in Madrid. "I thought I served pretty well and then used my forehand to dictate the points, but my movement was good too, and to feel comfortable with that on a court like this is critical," she said. "The ball does fly a little bit on these courts, so you need to feel like you're behind it and in control of it, or else it gets a bit out of control."
All of the other seeds survived their first round opponents, most notably No.2 seed Li Na, who dug out of two set points in the second set to beat Kirsten Flipkens, 6-1, 7-6(7), No.3 seed Agnieszka Radwanska, who outdid Eugenie Bouchard, 7-6(3), 6-2, No.4 seed Simona Halep, won won 10 games in a row to beat German qualifier Julia Goerges, 6-2, 6-0, and No.6 seed Jelena Jankovic, who was never broken in nine service games en route to a 6-4, 6-3 win over No.1 teenager Elina Svitolina.
No.13 seed Caroline Wozniacki, No.14 seed Carla Suárez Navarro and No.15 seed Sabine Lisicki moved on as well, with Suárez Navarro beating Yvonne Meusburger, 7-6(6), 6-4, for her WTA-leading 27th match win of the year. Suárez Navarro - the Spanish No.1 - just won her first WTA title in Oeiras.
The second round kicks off at the Premier Mandatory-level event on Tuesday.