After dropping a tight 69-minute first set, 6-4, Cibulkova got right back to work, racing through the second set, 6-2, and building a 4-1 lead in the third. The No.6-seeded Diyas found her range again, winning three games in a row to even it at 4-all, and even holding a point to hold for 5-4. But the No.1-seeded Cibulkova made one last push, breaking then holding one last time to seal it, 46 62 64.
"She played really, really well - it was a really big test," Cibulkova said. "Today was the first time it wasn't raining before the match, so it was really humid and the air was different. There was a really long game in the first set that I lost, and it really put me down physically - it made me feel really tired. It took me two or three games to get back and find my game, but I'm happy I managed to get it back.
"I was really showing my fighting spirit at the end. It's nice to win matches like this."
Cibulkova's win over Diyas was her WTA-leading 23rd match win of the season.
Awaiting the World No.10 in the semifinals will be No.3 seed and defending champion Karolina Pliskova, who blasted nine aces en route to a 64 64 victory over Cagla Buyukakcay. Buyukakcay, Turkey's No.1 player, was the first Turkish player ever to reach the quarterfinals of a WTA event.
The other semifinal will pit No.2 seed Zhang Shuai against No.3 seed Donna Vekic, after Zhang beat Magda Linette, 62 26 61, and Vekic beat No.4 seed Patricia Mayr-Achleitner, 64 75. Vekic hit 10 aces.
"I think I served really well in the first set - not so well in the second set, but it was important to keep the momentum going," Vekic said. "I'm very happy to be in the semifinals of a WTA event again. I've been to the semis twice before and I won both times, so I hope it's going to happen again here this week.
"I've been getting confidence since Indian Wells and Miami and I'm happy to continue the good run."
Both BMW Malaysian Open semifinals will be first-time meetings.