Sabalenka recorded a 6-1, 6-3 victory over Caterine Harrison in a first round match that saw her hit three aces and record six out of 13 break points.
Cornet referred dubbed herself as "the upset-girl" after ending Emma Raducanu's US Open title defence.
The Spaniard triumphed 4-6, 6-2, 6-3, 6-3 over Australian Rinky Hijikata at Flushing Meadows, where he is competing for the first time since winning the title in 2019.
The Dane will take on veteran US tennis player John Isner in what promises to be a fine battle between youth and experience.
The 11th seed had to work overtime to defeat the tenacious Daniel Altmaier in a five-set battle in the first round of the New York hard-court Grand Slam.
Rublev was pushed to the limit by Laslo Djere in the first round but the Russian edged out a 7-6 (7-5), 6-3, 3-6, 4-6, 6-4 victory.
On Thursday in the second round of 2022 US open Yibing Wu of China will face Nuno Borges of Portugal.
Leylah Fernandez and Liudmila Samsonova will face one another in a second round of the US Open 2022 on August 31.
Caroline Garcia and Anna Kalinskaya are scheduled to face one another in a second round match of the US Open 2022 on Wednesday, August 31.
Barbora Krejcikova and Aleksandra Krunic will face one another in a second round of the US Open 2022 on Wednesday, August 31.