It left Raducanu at 83 in this week’s new rankings but she had insisted she relished the “clean slate” it afforded her in her bid to return to the top of the game.
Raducanu saved all but one of four break points on her serve as she sunk Yastremska, who retired two points from defeat at 6-2 5-3.
“It has been really nice to be here. I came here early and it is a great place to have a tournament,” she said after victory.
“Nobody wants to win by retirement. She is a ferocious competitor. I fought hard to stay in the points. I am happy to be in the next round.”
The world No 83 faces either Elizabeth Mandlik - daughter of four-time Grand Slam champion Hana Mandlikova - or qualifier Anna-Lena Friedsam up next in the next round.
Raducanu’s goal since Flushing Meadows has been to target the WTA 250 events to rise up the rankings, saying after defeat to Cornet: “I mean, obviously it’s really disappointing. I’m really sad to leave here [US Open]; it’s probably my favourite tournament.
“But also, I mean, in a way, [I’m] happy because it’s a clean slate. I’m going to drop down the rankings, [and] climb my way back up.”