France forward Thuram opened the scoring midway through the first half and had a hand in two more strikes from Lautaro Martinez and Hakan Calhanoglu which helped continue Inter's perfect start to the new season.
"The whole team played well today, it was a good evening," said Thuram to DAZN.
"I'm really happy with my goal and key pass, I just want to help the team as much as I can."
Inter host Milan, who have also won their first three matches, in the first derby of the season immediately after the international break.
That match promises to be a blockbuster as both teams already look like strong contenders for the league title.
And Milan will be looking for revenge for a comprehensive defeat to their local rivals in last season's Champions League semi-finals.
Leading the line for Inter should be Thuram, who has slotted in brilliantly alongside Martinez since signing from Borussia Moenchengladbach this summer and returning to the country of his birth.
Thuram, 26, was born in Parma where his World Cup-winning father Lilian played for five seasons, winning the UEFA Cup and Italian Cup in 1999 as part of a star-studded outfit which also featured Italian icons Gianluigi Buffon and Fabio Cannavaro.
Martinez ended up with a brace to take his tally to five goals in three matches but it was Thuram who was crucial to seeing off woeful Fiorentina.
He crashed home a header in the 23rd minute from Federico Dimarco's pinpoint cross and could have had a hat-trick at half-time as close-range chances went begging.
However he rolled in Martinez for a simple finish eight minutes after the break and was then brought down by Fiorentina goalkeeper Oliver Christensen shortly afterwards to give Calhanoglu a chance from the penalty spot that he didn't waste.
Martinez capped off the scoring for Inter, who are yet to concede a goal, in the 73rd minute when he rammed home Juan Cuadrado's inviting low cross.
- Juve stroll past Empoli -
Juventus are two points behind the pace setters in third after their 2-0 win at bottom team Empoli, who are still pointless three weeks into the season.
Chiesa was picked in Luciano Spalletti's first Italy squad which will face North Macedonia and Ukraine in Euro 2024 qualifying.
And the 25-year-old showed the eye for goal that Juve coach Massimiliano Allegri has demanded from him when he sprinted through onto Arkadiusz Milik's through ball and carried on to roll home after being almost taken out by Empoli keeper Etrit Berisha.
The only sour note for Juve is that Paul Pogba could have picked up yet another injury after making an appearance from the bench, although Allegri said there would be no news until tests were carried out on Monday.
Roberto D'Aversa's team collected their second win of the season thanks to Nikola Krstovic's second goal since moving to southern Italy from Slovakia this summer and a stoppage time penalty from Gabriel Strefezza.