The Polish world No. 2 was defeated 3-6, 4-6 by the third-seeded American at the eight-player event in the Middle East on Tuesday.
Świątek opened her WTA Finals campaign with a 4-6, 7-5, 6-2 victory over the Czech Republic's Barbora Krejčiková.
She will now take on Jessica Pegula of the United States in her last group-stage match on Thursday.
The 2024 WTA Finals event began on November 2 and runs until Saturday.
Świątek, who is the defending WTA Finals champion, last month lost her world No. 1 spot to Belarusian Aryna Sabalenka after spending 125 weeks on top of the world rankings.
(gs)
Source: IAR, PAP, polskieradio24.pl