"I was just trying to get back to the rhythm which I lost after the first set and I'm really glad that I found a way," Kvitova said.
Pegula, who reached the quarterfinals at last month's Australian Open, was playing her seventh match in as many days after coming through qualifying in Doha.
"She is a very solid player from the baseline, and as we saw she can play some volleys as well, so it was very difficult," Kvitova added.
Kvitova will play in her first final since last year's Qatar Open, when she lost to Aryna Sabalenka. It will be a rematch of the 2018 final in Doha, when Kvitova beat Muguruza in three sets.
Muguruza reached Saturday's final by walkover. Azarenka hurt her lower back while warming up for her quarterfinal match against top-seeded Elina Svitolina on Thursday.
It will be Muguruza's second final of the season after losing to Ash Barty in the Yarra Valley Classic final last month.
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