Elena Baltacha, James Ward and Dan Evans are all just one win away from a place in the main draw following good results at Flushing Meadows.
Former British number one Baltacha thrashed Ukraine's Olga Savchuk 6-3 6-0 in New York.
Baltacha will now meet with Michelle Larcher de Brito, the Portuguese who beat Maria Sharapova at Wimbledon, on Friday.
The 30-year-old took control with a break of serve in the very first game and was the dominant player until rain arrived with the Scot 6-3 5-0 up.
The former top-50 star, who has slipped to 244th in the world rankings after a lengthy spell on the sidelines following foot surgery, didn't let a lengthy delay halt her progress though and she broke Savchuk's serve immediately when play resumed to book her place in the final qualifying round.
Ward also moved through with an impressive 2-6 6-4 6-4 victory over Germany's Mathias Bachinger.
British number two Ward, ranked 175th, had lost comfortably to his higher-ranked opponent in both their previous meetings and was outplayed in the first set here.
But the Londoner, who had never won a match at Flushing Meadows prior to his first-round victory, turned things around and is now one win away from qualifying at a grand slam for the second time.
His next opponent will be the higher-ranked Somdev Devvarman, of India.
In the late-night action, Evans made it three Britons to progress with a 7-5 1-6 6-3 victory over Flavio Cipolla. He will now face Spain's Adrian Menendez-Maceiras.
The one disappointment for the British contingent was defeat for Samantha Murray, beaten 6-4 7-5 by former world junior number one Taylor Townsend.