The 25-year-old, from Scarborough, whose late mother Laura rode for Britain in the 1992 Barcelona Olympics, topped her qualifying group with Everdale on a personal best grand prix score of 77.096 per cent.
Two riders from each of six groups – plus the next six-best finishers – contest Wednesday’s individual final.
And Fry’s outstanding performance under the floodlights also meant a strong start to British team hopes, with Charlotte Dujardin and Carl Hester completing a powerful trio.
Hester, who at 54 is Team GB’s oldest competitor in Tokyo, showcased all his experience with a solid display as heavy rain fell.
Gloucestershire-based Hester, riding in his sixth Olympics, finished fourth in Group C aboard En Vogue on 75.124 per cent.
And while Germany remain clear favourites for team gold, it was Fry who built the GB foundations in nerveless fashion.
“I was really happy with it,” she said. “It couldn’t have gone much better, to be honest.
“He (Everdale) definitely knew it was a big occasion. He was so concentrated today. It was such a great feeling.
“We have really kind of grown up together and built a really good partnership. I enjoyed every second of it, and he felt like he was enjoying it as well.
“You never know how it is going to feel when you go into the arena, and every arena is different, but I really trust him and he really trusts me.”
Defending champion Dujardin produced an inspired performance as she joined Fry and Hester Wednesday’s final.
Gold medallist at London 2012 and in Rio, Dujardin scored 80.963 per cent aboard major championship debutant Gio to complete a clean sweep of British qualifiers.
Her double Games winner Valegro was retired after Rio but Dujardin continues to work her magic, finishing second in Group F behind Germany’s Isabell Werth.
The trio also comfortably secured a place in tomorrow’s team final, going through as second-best qualifiers and on course for a third successive Olympic medal following gold in London and silver five years ago.
“I couldn’t have asked for any more from (Gio),” said Dujardin. “He is just unbelievable – he gives me everything he has got.”
“I really felt emotional towards the end of the test. He adjusts to whatever I ask and gives me his best.
“It could have been a full house today and he would have performed the same. He is such a pocket rocket.
“That to me, tonight, was as good as winning. For me, where he is right now with his training, he couldn’t have done any more.
“And that to me, is like a gold medal. It was one of those really special moments and I will remember it forever and a day.”
If Dujardin can reproduce such brilliance then she should be in contention for an individual medal.
And she will relish nothing more than taking on the significant double German threat of multiple Olympic gold medallist Werth and pre-Games favourites Von Bredow-Werndl.