Cibulkova twice came back from a break down in a tricky opening set, but the Slovak dominated the second to seal a spot in the last eight with a 6-4, 6-2 win in Budapest.
"Today was a pretty good performance from my side," Cibulkova told wtatennis.com. "Flipkens is always a very tricky player, she's playing with a different rhythm than all the other girls."
"I've played Larsson a couple of times; she's a good hitter," Cibulkova said. "And she's serving well, she has a good kick. So I'll have to be ready for it [on Thursday]."
No. 2 seed Zhang Shuai also advanced to the quarterfinals, with a hard-fought 2-6, 7-6 (4) 6-3 win over Jana Cepelova. Elsewhere, Mona Barthel shocked No. 3 seed Timea Babos 6-4, 4-6, 6-3 and Ysaline Bonaventure beat No. 8 seed Donna Vekic 6-4, 6-1.