Garcia was aggressive but not enough to stop Swiatek from continuing her winning streak, with the Pole at one point in the second set charging back from love-40 by winning five straight points en route to a semi-final spot.
Garcia, who won the pair's only previous meeting, managed to save just 20 percent of break points to Swiatek's 83 percent, losing in one hour and 23 minutes in Fort Worth, Texas.
Meanwhile, Gauff lost 7-6 (6) 6-3, marking her third loss to the lower-ranked opponent Kasatkina, who on Wednesday fell in straight sets to Swiatek.
Both players are making their WTA Finals debuts this year and despite Gauff's better ranking, the American has lost every professional match she has played against the Russian.
Kasatkina and Garcia will play on Saturday for the Tracy Austin Group's second-place spot and the chance to advance to the semifinals.