Latvia's Sevastova sprung a surprise early on, breaking twice to take a 4-0 lead before going on to win the first set.
Yet Kvitova came back to win 2-6, 6-2, 6-3 and reach the last four in Stuttgart for the third time in her career.
Along with Japanese world number one Naomi Osaka, Kvitova is one of the favourites in Stuttgart.
She will face either Victoria Azarenka or Anett Kontaveit in the semi-finals on Saturday, before potentially meeting Osaka in Sunday's final.
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