Jankovic struggled with the wind at Arthur Ashe Stadium on Saturday, at one point hitting a serve so badly the ball flew straight up into the air. The Serb had 41 unforced errors and just 13 winners.
Jankovic reached her only Grand Slam final at Flushing Meadows in 2008, but lost in the second round last year.
Kanepi kept her strong summer going by advancing to the fourth round at the U.S. Open for the first time. She made the quarterfinals at Wimbledon, then at Palermo in July she became the first Estonian woman to win a singles title.
The 25-year-old has moved up more than 100 places in the rankings since May 10.