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Maria Sakkari broke twice for a 5-1 cushion en route to capturing the first set, which meant Tunisian world number two Jabeur had no mathematical chance of advancing even if she had rallied back to victory.
Swiatek, who improved to 2-0 in this year's competition following her own 6-3, 6-2 win over Caroline Garcia, goes through as the winner of her group, while Gauff can no longer qualify for the semifinals.
The win continues a phenomenal season for Swiatek, who rose to world No. 1 in April and has won eight titles, including two Grand Slams at Roland Garros and Flushing Meadows this year.
Sakkari battled past world No. 3 Pegula 7-6(6) 7-6(4) to record her first win over a top-five opponent this year.
She will join Iga Swiatek, Ons Jabeur, Jessica Pegula, Coco Gauff, Caroline Garcia, Aryna Sabalenka and Daria Kasatkina at the season finale.
Greek fourth seed Sakkari kept alive her hopes of making the Finals by surviving an early scare and fighting back from a set down to beat American Danielle Collins 5-7, 6-3, 6-3.
The defeat was another blow to Barca and manager Xavi Hernandez after they were left on the brink of Champions League elimination following a draw with Inter Milan last week.
The home win lifted Inter to second place in Group C on six points, three behind leaders Bayern Munich and three in front of Barcelona.
Real Madrid are level with rivals Barcelona on 19 points at the top of standings, with Barca ahead on goal difference.
'I struggled to win my first WTA title. It took me time. So I believe this will take me time,' said the Tunisian.