AFPSecond seeded Cibulkova wasted little time in booking her place in the last eight, where she will now play Urszula Radwanska.
Radwanska, in good form in California, was even more ruthless with a 6-2 6-1 demolition job on home hope Melanie Oudin.
Fifth seed Christina McHale set up a quarter-final against top seed Marion Bartoli with a 4-6 6-4 6-4 win over Misaki Doi of Japan.
And completing the last-eight line-up was Jelena Jankovic, the third seed from Serbia seeing off Melinda Czink of Hungary 2-6 6-4 6-4 to book a date with Yung-Jan Chan of Chinese Taipei.
Only five games were played at WTA Bastad on Thursday as rain destroyed the action in Sweden.
Third seeded Spaniard Anabel Medina Garrigues was 3-1 up in the first set against Sweden’s Johanna Larsson, with France’s Mathilde Johansson one game up against Israel’s Shahar Peer in their second-round match before the heavens opened.
