The 17-year-old Tasmanian stopped the clock in 24mins 2.04secs at the end of the 16.1km course held in and around Bergen.
Pirrone won the title in 23mins 19 secs - 42 seconds faster than Fasnacht and seven ahead of compatriot Vigilia.
"I didn't know what to expect today I just did my best and I'm really happy with getting on the podium," Fasnacht said. "It's been a pretty phenomenal year really from one thing to the next."
Fasnacht will represent Australia in the under 19 women's road race on Friday.
Under 19 Women's TT
1 Elena Pirrone (ITA) 23min 19.72sec
2 Alessia Vigilia (ITA) 0:6:38
3 Madeleine Fasnacht (AUS) 0:42.32
In the men's under 23 event, Callum Scotson rode consistently to finish fifth behind Tom Wirtgen of Luxembourg, missing a spot on the podium by just five seconds.
The race was won by Norwegian Mikkel Bjerg in a time of 47min 6min over the 37km course, in front of American Brandon McNulty and Frenchman Corentin Ermenault.
"For sure it is a little disappointing to finish so close to the podium but that is racing," Scotson said. "In a time trial what you put out there on the course is what you finish with, so even if you are close you have to settle with what you did and I enjoy the event for that reason."
Scotson will line up alongside Robert Stannard, Jai Hindley and Michael Storer in the under 23 men's road race on Friday.
Under 23 men's TT
1 Mikkel Bjerg (DEN) 47min 06.48min
2 Brandon McNulty (USA) 0:01:05
3 Corentin Ermenault (FRA) 0:01:16
5 Callum Scotson (AUS) 0:01:21