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Sabalenka has enjoyed a spectacular season, defending her Australian Open title in January and adding the US Open trophy to her cabinet last month, as well as enjoying victories in Cincinnati and Wuhan.
Pegula looked in cruise control in the second set as she broke Swiatek again in the third game.
Swiatek showcased her all-court game in a straightforward 6-4 6-1 win over Russian Liudmila Samsonova to open the evening session.
The five-time Grand Slam champion blamed stress and a lack of time between matches for her performance.
Kazakh Yulia Putintseva who battled back superbly won the third-round clash 3-6 6-1 6-2 against Swiatek.
Djokovic defeated 277th-ranked Jacob Fearnley while top seed Swiatek, fresh from her Roland Garros success, beat Croatian Petra Martic 6-4 6-3.
Men's defending champion Carlos Alcaraz, seeded three, will start against Estonian qualifier Mark Lajal and finds himself in the same half of the draw as top seed Jannik Sinner.
The World No 1 defeated the Italian 6-2, 6-1.
Swiatek defeated Coco Gauff 6-2, 6-4 while Paolini downed Andreeva 6-3, 6-1.
Second seed Sinner kept his hopes of taking Djokovic's top ranking alive with a battling 2-6 6-3 6-2 6-1 win over local favourite Corentin Moutet.
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