With mentor Martina Hingis cheering from the stands, 17-year-old Belinda Bencic became the youngest US Open quarterfinalist since Hingis herself in 1997.
Playing on Arthur Ashe Stadium, ninth-seeded Jelena Jankovic was far more rattled than an opponent 12 years her junior.
Bencic won 7-6 (6), 6-3 on Monday.
''I think she had all the pressure because she needed to win,'' Bencic said. ''I could just enjoy.''
Bencic saved three set points in the first, as Jankovic twice failed to serve out the set.
She is the youngest player to reach a Grand Slam quarterfinal since Nicole Vaidisova at the 2006 French Open.
Hingis was 16 when she won the US Open in 1997 - Bencic was six months old at the time.
Hingis' mother, Melanie Molitor, coaches Bencic.
Before the match, Hingis gave Bencic some advice on how to play Jankovic.
''She told me to hold the rallies,'' Bencic said. ''I have to be aggressive. I had to pay attention to her backhand down the line. ... So I tried to push it to her forehand.''
She next faces China's Peng Shuai, another unseeded player making her major quarterfinal debut, for a spot in the semis.
The difference is that Peng is 28 years old. The 58th-ranked Swiss teen has now defeated top-10 players in consecutive matches after upsetting sixth-seeded Angelique Kerber in the third round.