World No.2 Swiatek made 36 unforced errors in the last two sets while Rybakina made 17, with the Kazakh player getting her first win over the six-time grand slam champion in their last five meetings to edge closer to the semi-finals.
"It was difficult to be down, but in the second set I pushed myself, the serve improved. Really happy that I stepped in and played better in each point," said Rybakina, who beat Amanda Anisimova in straight sets on Saturday.
Swiatek made a dominant start to win the first three games on Monday as she targeted Rybakina's body with her serves, while the sixth seed's backhand returns often hit the net. Swiatek looked in control as she took the first set 6-3.
However, the Pole's double fault and an unforced error gave an early break to Rybakina, who then held her serve with an ace to go 3-0 up in the second set.
Wimbledon champion Swiatek was left frustrated when she made three successive unforced errors as Rybakina broke again to go 5-1 up, sealing the set in her favour.
Swiatek continued to struggle, making 17 more unforced errors as Rybakina handed her a bagel in the third set.
Rybakina will face Madison Keys in her last match in the round-robin Group Serena Williams while Swiatek, who beat Keys on Saturday, takes on Anisimova.
Americans Keys and Anisimova play each other later on Monday (local time).
