Rogers rallied from down 5-2 in the third set to upset Barty 6-2, 1-6, 7-5 (5) on Saturday night for the biggest win of the 28-year-old's career.
Her win streak may not yet rival the streaks set by Rafael Nadal, who won his first 31 matches in the French Open but they beat the alternative.
Djokovic moved into the fourth round at Flushing Meadows for the 14th consecutive appearance, coming back to beat Kei Nishikori 6-7 (4), 6-3, 6-3, 6-2.
The 11th-seeded Bencic eliminated No. 23 Jessica Pegula 6-2, 6-4 in a rematch from the Summer Games.
The sixth-seeded Canadian had little trouble advancing with a 6-1, 6-2 victory over 104th-ranked Greet Minnen of Belgium
The unseeded Mirza and Ram lost 3-6 6-3 7-10 to their opponents in just 61 minutes on Friday night.
Osaka conceded a defeat against Canadian teenager Leylah Fernandez, who came up with an inspired performance on Friday evening to win 5-7, 7-6(2), 6-4.
Second seed Daniil Medvedev continued his perfect run in New York, cruising past Spaniard Pablo Andujar 6-0, 6-4, 6-3 to reach the fourth round for the third straight year.
Alcaraz won 6-3, 4-6, 7-6 (2), 0-6, 7-6 (5) in just over four hours to become the youngest man in the fourth round at Flushing Meadows since Pete Sampras and Michael Chang in 1989.
Osaka's title defense at the U.S. Open was over in the third round with a 5-7, 6-7 (2), 6-4 loss Friday night to Leylah Fernandez, an 18-year-old from Canada
The world No. 4 has been dominant on serve this week, not offering a single break point opportunity to Sam Querrey in the first round.
Djokovic registered a 6-2 6-3 6-2 win over Dutchman Tallon Griekspoor to advance to the third round in US Open.
World No.1 Barty of Australia staved off a late challenge by 18-year-old Clara Tauson of Denmark, 6-1, 7-5, to book her spot in the third round.
Remnants of Ida hurricane knocked down tree limbs and causing flooding around the tournament grounds while a retractable roof at the US Open was no match for the heavy rain and wind.
Djokovic's second-round match is against Tallon Griekspoor, who was moved into the main draw when Federer had to withdraw because of a knee injury.
The third-seeded Tsitsipas hit 27 aces and beat Mannarino 6-3, 6-4, 6-7 (4), 6-0 at Arthur Ashe Stadium.
Sloane Stephens entered the third round with a 6-4, 6-2 victory over 21st seed Coco Gauff.
The No. 12 seed rolled to a 6-3, 6-1 victory over Kristina Kucova at Arthur Ashe Stadium, where their match was moved after Naomi Osaka's opponent withdrew from their scheduled match.
The ninth-seeded Muguruza, a two-time Grand Slam champion, beat Andrea Petkovic 6-4, 6-2. She could next face No. 18 seed Victoria Azarenka
Osaka had been scheduled to face Olga Danilovic of Serbia in the first match of the day at Arthur Ashe Stadium.
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