Kvitova, the second seed in New Haven, downed fellow Czech Barbora Zahlavova Strycova in their quarter-final 6-4 6-1.
Zahlavova Strycova started the better in the WTA Premier hard-court clash, breaking serve in the third game and preserving that lead with comfortable holds.
Kvitova, though, broke back in the eighth game, and with Zahlavova Strycova serving to stay in the set, the two-time Wimbledon winner struck again to take the first set.
From there, it was smooth sailing for Kvitova, who broke in the fourth and sixth games to coast to victory in one hour eight minutes.
Stosur won an all-wildcard battle over Belgium's Kirsten Flipkens, the Australian triumphant 6-3 4-6 6-3.
Ranked 25th, Stosur is finding form at the right time of year ahead of next week's US Open, and the 2011 champion at Flushing Meadows hit 32 winners in her win over a brave Flipkens.
On the other side of the draw, unseeded pair Camila Giorgi and Magdalena Rybarikova progressed.
Slovakia's Rybarikova, who ousted top seed Simona Halep earlier in the tournament, continued her run with a 7-5 0-6 6-4 victory over American Alison Riske.
Rybarikova won just 10 points in the second set, but overcame the glitch to reach the last four of a WTA Tour event for the second time this season.
Playing off for a spot in the final will be Italy's Giorgi, who outmuscled Spain's Garbine Muguruza 6-4 6-7 (4-7) 6-2.
Giorgi served 19 double faults - including 10 in the second set - but still managed to progress in two hours 14 minutes.