Gauff was already guaranteed to make the semis, but five-time grand slam champion Swiatek needed the American to beat Wimbledon champ Krejcikova, who had required a victory herself to progress.
Gauff will now face world No.1 Aryna Sabalenka in a blockbuster semi-final, while Krejcikova will take on China's Olympic champion Zheng Qinwen in the other.
Wimbledon champ Barbora Krejcikova is into the semi-finals in Riyadh. (AP PHOTO)
The world No.13 Krejcikova took a tight first set, which lasted 54 minutes, after saving four break points, wrapping it up with a powerful backhand that zipped down the line.
Former US Open champion Gauff, who had not dropped a set in the tournament before the contest, was hurt by unforced errors — 23 alone in the opener.
The second set was once again a close affair, but the Czech held her nerve to secure the win in one hour and 42 minutes.
"This is a big win for me and really happy with how I played and it was a really good match," the 27-year-old Krejcikova said.
"It's tough, it was up and down. The Wimbledon victory is the highest point in my career so far.
"Being here and reaching the semi-final, it's something unimaginable. I'm really proud of myself and I'm looking forward to the new challenges."
Krejcikova is the lowest-ranked player to book a spot in the semis at the WTA Finals since Sandrine Testud (14) in 2001.
Earlier Swiatek had produced a ruthless performance to dismantle Daria Kasatkina 6-1 6-0, wasting little time in asserting herself as she raced to a 5-0 lead in the opening set which she wrapped up with an ace.
Having replaced Jessica Pegula after the American withdrew due to a left knee injury, world No.9 Kasatkina was demolished in the second set as Swiatek sealed the win in 51 minutes, making it the fastest match at the WTA Finals in eight years.
Swiatek won 72 per cent of her points on serve and thumped 15 winners as she extended her head-to-head advantage over the 27-year-old Russian to 6-1.
Kasatkina is not the first player to be steamrollered at the WTA Finals by Swiatek, who took her tally of 6-0 set wins at the tournament to five.
The 23-year-old Pole equalled Serena Williams' total of 6-0 set wins at the event and is now only behind greats Martina Navratilova (12), Chris Evert and Steffi Graf (both seven).
