The fifth-seeded Italian advanced with a 6-3 6-4 victory over Kazakhstan's No.30 seed Yulia Putintseva on Saturday.
Paolini, 28, had never made it past the second round in 16 appearances at majors entering this season. But she reached the fourth round at the Australian Open in January, before being the runner-up at both the French Open in June and Wimbledon in July.
Now she is once again into week two after compiling 13 of her 22 winners off the forehand side against Putintseva at Louis Armstrong Stadium.
Paolini will meet 2023 French Open finalist Karolina Muchova on Monday for a berth in the quarter-finals at Flushing Meadows.
Jessica Pegula's strong serving and smothering defence led to a textbook 6-3 6-3 win for the sixth seed over Spain's Jessica Bouzas Maneiro.
The American, who struggled with injuries earlier in the year, produced her best form of the tournament so far, winning 89 per cent of her first serve points, cracking 13 winners and breaking her opponent four times.
"I just played solid," Pegula.
"I didn't do anything crazy. I didn't do anything bad or that amazing. I think I was just very consistent.
"Even when she got back into that second set, I was able to find some energy, get a hold and close it out pretty quick, so I'm proud of that."
Pegula, 30, missed this year's French Open to recover from injuries and after suffering an early exit at Wimbledon, she triumphed at this month's Canadian Open.
The Buffalo, New York native has said she would relish winning her first Grand Slam on home soil and opted not to compete in doubles at Flushing Meadows this year to focus on her singles game.
She has flashed an improved serve and speedy defense through her first three matches and will next face Diana Shnaider, a 6-2 6-2 winner over Italian veteran Sara Errani.
With AP
