The fifth-seeded Dane dropped seven games in beating defending champion Jankovic 6-3 6-4 and next faces the unseeded Kristina Mladenovic.
She saw off Daria Gavriolva, beating the eighth seed 7-5 6-3.
"I was very happy with the way I played - I think it was high level, from both of us," Wozniacki told the ATP's official website afterwards.
US Open
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"Wins like this always give a lot of confidence. I'm really pleased that I was able to win in two sets."
In Linz, Austria, Madison Keys withdrew from her semi-final of the Generali Ladies event against Viktorija Golubic citing illness.
The third seed's withdrawal gave Golubic a route to the final against Slovakian Dominika Cibulkova who saw off Carla Suarez Navarro 6-4 6-3.
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US Open
'It's not acceptable' - Djokovic gets 'unfair treatment' compared to Federer and Nadal, says Becker
16/09/2021 AT 13:31