Swiatek has been in top form in New York having dropped just eight games through her two matches and will be heavily favoured when she faces Slovenian qualifier and good friend Kaja Juvan in the second match at Louis Armstrong Stadium.
The Pole, who has held the world number one ranking since April 2022, won their two previous meetings, most recently in the first round of the 2021 French Open, while Juvan has matched her career-best showing at a Grand Slam this week.
Djokovic, who is seeking a 24th Grand Slam title to equal Margaret Court's record, will close out the evening session at Arthur Ashe Stadium when he faces fellow Serbian Laslo Djere, the 32nd seed.
Second seed Djokovic enters the match with a 40-5 win/loss record for the season and fresh off collecting a record-extending 39th ATP Masters 1000 crown at a US Open tune-up event in Cincinnati where he beat world number one Carlos Alcaraz in the final.
"At 36 years of age, after 20 years of coming to New York, I still have the hunger to play my best tennis on this court," said Djokovic.
"I have the experience and understanding of what needs to be done in the important moments. Preserving the energy and focusing on the present moment."
Top-ranked Americans Taylor Fritz and Frances Tiafoe are also in action with both looking to bolster their hopes of becoming the first U.S. man to win a Grand Slam in 20 years.
Standing in Tiafoe's way will be 35-year-old Frenchman Adrian Mannarino, the 22nd seed, while Fritz has a meeting with Czech qualifier Jakub Mensik.
Tiafoe has failed to advance past the third round of a Grand Slam since his run to the New York semis last year and had a less-than-stellar lead-up to the US Open but has reached the third round without dropping a set.
Fritz has never before reached the last 16 in New York but has also enjoyed a smooth passage into the third round having dropped just five games in each of his two matches.
Former Australian Open champion Caroline Wozniacki, in only her third event since returning to tennis after more than three years away to start a family, will look to extend her New York stay when she faces American Jennifer Brady.
In the second round, a resurgent Wozniacki earned her first top-20 win in nearly five years with a straight-sets upset of 11th seed Petra Kvitova.
"I've been feeling very comfortable here in New York in general," said former world number one Wozniacki.
"Ever since I arrived here, it's just something about the courts, everything else, that have made me feel good."
Among the other high-profile names in action are American sixth seed Coco Gauff, who kicks off the night session at Arthur Ashe Stadium against Belgian Elise Mertens, and former Wimbledon champion Elena Rybakina, the fourth seed, who faces Romania's Sorana Cirstea under the Louis Armstrong Stadium lights.
