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Jabeur, the No.5 seed at Flushing Meadows, had previously fallen short of making the second week in the season's final grand slam, having reached the third round in three successive years between 2019 and 2021.
But the Tunisian world No.5 ended that wait with a 4-6 6-4 6-3 defeat of American Rogers.
Jabeur reached the final at Wimbledon this year, her first appearance in a Major showpiece match, but lost to Elena Rybakina.
She has made it to the fourth round of the grand slams six times, having managed quarter-final runs at Wimbledon (2021) and the Australian Open (2020).
Another US Open fourth-round debutant awaits Jabeur in the form of Veronika Kudermetova, who despatched Dalma Galfi 6-2 6-0.
Kudermetova's victory took just 46 minutes, making it the shortest match of the tournament.