Tien is the first 19-year-old American to reach the fourth round at the Australian Open since 14-time Grand Slam winner Pete Sampras in 1990.
He is one of a trio of teenagers who have impressed with wins over top-10 players in Melbourne.
Brazil’s Joao Fonseca, 18, stunned Russian Andrey Rublev in the first round, then 19-year-old Czech Jakub Mensik knocked out Norway’s Casper Ruud in the second round.
But while both Fonseca and Mensik have fallen, Tien has advanced to set up a meeting with Italy’s Lorenzo Sonego.
“It feels great, obviously,” said Tien.
“This has exceeded my expectations, what I was hoping for coming into this week.
“You go into every match believing you can win, but to be in the second week is amazing.”
Meanwhile Monfils, a showman and a crowd favourite, continued his rich vein of recent form.
His win over 27-year-old Fritz follows victory at the ASB Classic in Auckland earlier this month, when he became the oldest winner of an ATP Tour singles title.
After serving an ace – his 24th of the match – to see out victory, Monfils danced in celebration before pumping his chest and roaring to the stands.
“I have a strong belief I can still do some damage,” Monfils said.
“He started strong but I felt I could move great today.”
Monfils’ victory came before his wife Elina Svitolina won her third-round tie against Jasmine Paolini on the same court.
“I think I warmed up the court for her,” Monfils joked.
“She plays the world number four so it will be tough for her but I hope she will smash this one.”
Monfils will play American 21st seed Ben Shelton after he beat Italy’s Lorenzo Musetti 6-3 3-6 6-4 7-6 (7-5).