Six-time champion Serena, 36, beat German world 101 Carina Witthoft 6-2 6-2, while twice champion Venus saw off Italy’s Camila Giorgi 6-4 7-5.
The last time the Americans played each other at a Grand Slam was in the final of the 2017 Australian Open, which Serena won when eight weeks pregnant.
Serena missed the US Open last year, giving birth to daughter Olympia shortly after the tournament started. She reached the Wimbledon final in July.
Chasing a record-equalling 24th Grand Slam singles title, Serena unleashed 30 winners and 13 aces on her way to victory over Witthoft and sealed victory when the German netted a forehand.
While Serena wrapped up her win in one hour seven minutes, it took Venus an extra 45 minutes to beat Giorgi.