Belarusian Sabalenka, who could become the first woman since Serena Williams in 2012-14 to win the tournament three years in a row, defeated Colombian Camila Osorio 6-2, 6-4.
Alcaraz, seeded second in the men's singles, then defeated Russia's Roman Safiullin at Arthur Ashe Stadium in Flushing Meadows. The Spaniard was playing his first singles match since April.
The wrist injury showed no signs of wear and tear. Alcaraz won in straight sets - 6-4, 6-4, 6-4.
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