Garcia came out on top in an almighty battle with Kasatkina to complete the WTA Finals semi-final line-up.
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.
The Frenchwoman prevailed 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 before 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.
However, Garcia held her nerve in the tiebreaker to secure victory on her second match point.
Garcia and Sakkari will do battle for a place in the final with the winner to face top-ranked Iga Swiatek or Aryna Sabalenka.