The diminutive Cibulkova swept past Germany's world number 31 Laura Siegemund 6-2, 6-0.
The diminutive Cibulkova, who upset world number one Angelique Kerber to win the WTA finals in Singapore last October, swept past Germany's world number 31 Laura Siegemund 6-2, 6-0.
Cibulkova, who lost to China's Li Na in the 2014 Australian Open final, will next play Canadian wild card Eugenie Bouchard in the second round of the WTA lead-in tournament to next week's Australian Open.
"When you start a season, you always start with some confidence, not doubt, but you always need to get into this match rhythm," said Cibulkova.
"It's not easy if I would expect myself to play like I did in the (WTA) final against Kerber, I think that would be too much expectation.
"This is the time of the year when you just have to warm up yourself in the matches."
Cibulkova, who lost to Agnieszka Radwanska in the Sydney final four years ago, was knocked out in the quarter-finals of last week's Brisbane International by France's Alize Cornet in straight sets.
Kerber and Radwanska, the top two seeds, have a bye into the second round at Sydney.
Former world number one and seventh seed Caroline Wozniacki dumped Olympic champion and last year's finalist Monica Puig out of the tournament 6-3, 2-6, 6-4.
Puig, who lost to Russia's Svetlana Kuznetsova in last year's final, had 12 break point opportunities but could only convert three, while Wozniacki put away three of four break points.
British sixth seed Johanna Konta was too strong for Australian Arina Rodionova 6-3, 6-4 and fellow Australian Sam Stosur again bombed out in the first round, going out 6-3, 6-1 to Russia's Anastasia Pavlyuchenkova.
"It was tough conditions out there. I don't really know what to say," said Stosur, who hasn't won a match in almost five months.
"I don't feel like I played bad. I don't feel like I played obviously as well as I can. It was just kind of done, and that was it."
Russian eighth seed Elena Vesnina withdrew with a lower back injury when trailing American Coco Vandeweghe 6-2, 4-0.
In the men's draw, Australian qualifier Matthew Barton eliminated British number two Kyle Edmund 7-6 (7/3) 7-6 (7/5) and will next face either Gilles Muller or Alexandr Dolgopolov.