Radwanska won 6-3, 7-5 on Saturday to make the fourth round at Flushing Meadows for the first time since 2008. The Pole was broken four times, but she converted six of seven break-point chances against the 30th-seeded Jankovic.
Jankovic, who ascended to No. 1 in the rankings and was the U.S. Open runner-up in 2008, had 37 unforced errors to 15 for Radwanska.
Radwanska needed 1 hour, 38 minutes to win the two sets. She reached her first Grand Slam final this year at Wimbledon, losing to Serena Williams. Her next opponent is 20th-seeded Roberta Vinci, who beat No. 13 seed Dominika Cibulkova 6-2, 7-5.