Jabeur rallies to advance at US Open
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Fifth seed Jabeur, who made history at Wimbledon in July after becoming the first African woman to reach the final at the All England Club, came from behind to advance 4-6, 6-4, 6-3.
The 28-year-old will face Russia's Veronika Kudermetova in the fourth round.
In nine previous appearances in New York she had not got beyond the third round.
"Crazy, crazy match," Jabeur said after her win. "Shelby plays really well.
"I'm glad I got the win. It was difficult to adapt to how well she was playing. I was happy that I kept fighting to the end and got the win."
Rogers, the 31st seed, reached the quarter-finals in New York two years ago, her best performance at the tournament.
The right-hander from South Carolina flirted with a remarkable comeback in the third set after saving four match points before holding serve for 5-2.
She then broke Jabeur to reduce the deficit to 5-3, but lost her next service game to love as the Tunisian advanced.