Both 18-year-old players had injury time-outs during the match with Cibulkova needing treatment to a lower back and hip complaint, and Radwanska requiring the trainer to attend to a foot injury.
"It was the toughest match I've played at the tournament so far," Radwanska told Al Jazeera Sport in her courtside interview.
"I'm still shaking because it was such a good match.
"I was more focused towards the end. I'm very happy."
"It was the toughest match I've played at the tournament so far."
Both players struggled to hold their serves in cool and breezy conditions, with Radwanska winning the first set, but then going down 1-5 in the second.
The Polish 16th seed fought back as Cibulkova failed to take advantage when serving for the set on three occasions, but the Slovakian eventually levelled the match at one set apiece after winning the tie-break 7-1.
There were several breaks of serve in the deciding set before Radwanska, ranked 25 places higher than her opponent, closed out the match to move into the semis.
Maria does it easy
Meanwhile on court one, Zvonereva began slowly but improved to defeat her Austrian opponent Sybille Bammer 2-6, 6-2, 6-0 and move through to the final four.
Zvonereva, ranked 27 in the world, will meet the winner of the quarter-final between China's Na Li and Serbian third seed Jelena Jankovic.
|"I've got to be ready, be focused for every match. When I step out on to the court it's all business for me."|
Later on centre court, Sharapova breezed past Denmark's Wozniacki 6-0, 6-1 to storm into the semis where she will meet Radwanska on Saturday.
Sharapova, fresh from her third grand slam win at the Australian Open, totally outclassed the 17-year-old Wozniacki, who is ranked 53 in the world.
When asked if she thought it was an easy win against a lesser opponent, Sharapova replied: "It was easy because I did all the right things.
"I've got to be ready, be focused for every match. When I step out on to the court it's all business for me."
Big names bow out
Radwanska has the recent edge over her more heralded opponent, with their last meeting resulting in a 6-4, 1-6, 6-2 win to the Pole in the third round of last year's US Open.
"The last time I played her, she beat me at the US Open last year," Sharapova said of her semi-final adversary.
"I don’t like losing to the same person twice so I'm glad I've got another chance against her."
The Qatar Open, recently elevated to Tier 1 status, has a prize pool of $2.5 million, and with the likes of top seed Ana Ivanovic, second seed Svetlana Kuznetsova, Anna Chakvetadze and Venus Williams already out, there is a great opportunity for a lower-ranked player to win big.