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Swiatek showcased her all-court game in a straightforward 6-4 6-1 win over Russian Liudmila Samsonova to open the evening session.
The second-seeded Bopanna-Ebden pair lost to the 16th seed Argentine combo of Maximo Gonzalez and Andres Molteni in 66 minutes.
The sixth-seeded American Pegula, who struggled with injuries earlier in the year, produced her best form of the tournament so far.
Djokovic will end the year without a major for the first time since 2017.
The former champion was stunned by Dutchman Botic van de Zandschulp in straight sets.
Osaka lost to Karolina Muchova in the second round, unable to get to grips with the Czech's superb serve-and-volley tennis.
The Italian defeated American Alex Michelsen 6-4 6-0 6-2.
Romanian qualifier Elena-Gabriela Ruse won 6-4, 7-5 to reach the third round.
The green-and-white outfit drew inspiration from Japan's colourful, playful and self-expressive Harajuku style.
The 184th-ranked Evans, once the British number one, beat world number 22 Khachanov in five hours and 35 minutes.
Results 11-20 of 243
