The 26-year-old had first beaten lucky loser Elina Avanesyan in straight sets in their quarter-final on Saturday morning after play was cancelled due to heavy rain on Friday.
Vekic made it two wins from her Saturday matches on her fourth match point with another forehand winner flying past her opponent, who also had to play twice in a day, having earlier beaten Marketa Vondrousova in her last-eight match.
Sakkari has now lost all five of her semi-finals this season.
Vekic will face either Russian Ekaterina Alexandrova or Czech Petra Kvitova in Sunday's final.
Reporting by Karolos Grohmann; Editing by Ken FerrisOur Standards: The Thomson Reuters Trust Principles.
Persons:
Donna Vekic, Greece's Maria Sakkari, Lisi Niesner BERLIN, Maria Sakkari, Elina Avanesyan, Sakkari, Vekic, Marketa Vondrousova, Ekaterina Alexandrova, Czech Petra Kvitova, Karolos Grohmann, Ken Ferris
Organizations:
Tennis Club, Thomson
Locations:
Berlin, Germany, Greece, Czech