The winner of the Tracy Austin Group match in Fort Worth knew they would face Maria Sakkari in the last four and it was world number six Garcia who got the job done.
Frenchwoman Garcia won 4-6 6-1 7-6 (7-5) in a topsy-turvy contest that was finally settled in two hours and 27 minutes.
Kasatkina won four games in a row to take the opening set, but sixth seed Garcia stormed back to level the match in emphatic fashion as her aggressive approach paid off.
Russian Kasatkina twice came from a break down in a tense decider and fended off six break points in the ninth game of the final set to hold for a 5-4 lead, but Garcia held her nerve in the tie-break to advance.
Garcia and Sakkari will do battle for a place in the final on Sunday, with the winner facing either Iga Swiatek or Aryna Sabalenka.
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