Venus and Putz went up against the Portuguese duo of Francisco Cabral and Nuno Borges in the second round and emerged victorious by a score of 6-4, 7-6 (7-3).
Ram and Salisbury faced the Italian duo of Fabio Fognini and Simone Bolelli in the round of 16 and came out 6-1, 7-5 victors.
Skupski and Koolhof were up against home favourites Nathaniel Lammons and Jackson Withrow in the second round.
Casper Ruud rebounded from a mid-match hiccup to beat French lucky loser Corentin Moutet 6-1, 6-2, 6-7(4), 6-2 on Sunday to reach the US Open quarter-finals for the first time.
The Belarusian tennis player hit two aces and converted five out of 11 break points to take a 6-3, 6-0 victory.
Despite Williams' valiant efforts, Tomljanovic prevailed, with the two-time Wimbledon quarter-finalist going to the fourth round at Flushing Meadows.
The 19th seed went up against Cristina Bucsa in the second round of the Grand Slam and won by a score of 6-2, 7-5.
The Pole hit one ace and recorded four out of 12 break points to win 6-3, 6-2 against Sloane Stephens to make it through to the third round of the Grand Slam.
At the beginning of the Grand Slam, Sabalenka had said that she considered taking a break from the sport.
In the first round, Pliskova was pushed to the limit by Magda Linette but managed to emerge victorious by a score of 6-2, 4-6, 7-6 (10-8).