Former US Open champion Coco Gauff then eased past fellow American Jessica Pegula 6-3 6-2 in the other Orange Group match in Sunday's opening round-robin matches.
Swiatek lost in the US Open quarter-finals in September and was leapfrogged in the world rankings by Aryna Sabalenka after she skipped the WTA Tour's Asian swing due to fatigue.
Coco Gauff won her match in Riyadh in straight sets. (AP PHOTO)
The 23-year-old, who is looking to reclaim top spot in the Saudi Arabian capital, dropped her serve early and was unable to gain a foothold as Wimbledon champion Krejcikova ran away with the first set.
"It wasn't easy. At the beginning I felt a bit rusty, but I'm happy I found a way to play a little bit more solid," Swiatek said.
"I didn't feel great at the beginning. Barbora also used that. The score went her way pretty quickly.
"I knew it was tight even in the first set and I had my chances so I just wanted to use them the next time."
Krejcikova broke twice in the second set after two double faults by an increasingly off-colour Swiatek, whose fans at the King Saud University Indoor Arena sensed a big upset and looked to lift the French Open champion.
"I heard it for sure. I missed that. In tough moments today when I heard you guys screaming, it helped me. Thank you for the support. Even though at the beginning my game wasn't nice, you guys still believed."
Swiatek came out swinging from 3-0 down and moved ahead for the first time with a thumping backhand winner, before levelling the match at one set apiece.
She held to love for a 5-0 lead in the decider as Krejcikova struggled with a lower back problem, and withstood a late charge to close out victory.
With Sabalenka defeating Zheng Qinwen on Saturday, Swiatek will need to retain the trophy after winning at least two round-robin matches to have any chance of overtaking the Belarusian and finishing as year-end world number one.
Elena Rybakina will look to rebound from her opening loss when she plays Zheng on Monday before top seed Sabalenka takes on French Open and Wimbledon finalist Jasmine Paolini in the Purple Group.
