The clubs reconvene for the second leg at Stadio Artemio Franchi, where the aggregate winner will go into Friday's group stage draw.
Match preview
Having missed out to West Ham in June's Europa Conference League decider, Fiorentina began the long route towards the 2024 final last Thursday, when they ventured to Vienna for the first leg of their qualifying playoff.
After coming up just short both in Europe and last season's Coppa Italia, the team that finished only eighth in Serie A took advantage of UEFA banning Juventus from continental competition to book a Conference League return.
Highly-rated coach Vincenzo Italiano made only one change from the XI that saw off promoted Genoa on the opening day of their league campaign, but his decision to prioritise continuity over fresh legs did not pan out perfectly at Allianz Stadion.
In front of a large crowd in the Austrian capital, Fiorentina midfielder Rolando Mandragora was penalised for a first-half foul in his own penalty area, allowing Rapid Vienna's Marco Grull to convert the subsequent spot-kick; ultimately deciding the game.
Perhaps such a result was no surprise to fans of the Viola, as their team won just six away games in the league last season - but then failing to put away Lecce at Stadio Franchi on Sunday served a blow to hopes of building momentum in Serie A.
After Nicolas Gonzalez netted his fourth successive headed goal and Alfred Duncan added a second before the break, three points seemed assured for Italiano's side. A couple of second-half lapses, however, allowed their Puglian visitors to pull level and take a 2-2 draw home from Tuscany.
Following their first-leg success last Thursday, Rapid also had to settle for a point at the weekend, as they could not turn their dominance into a third Austrian Bundesliga win of the season at home to WSG Tirol.
Die Grun-Weissen's 1-1 draw, though, extends their unbeaten run to four games, including Conference League victories over Fiorentina and third qualifying round victims Debrecen, of Hungary.
Compared to inevitable league leaders Red Bull Salzburg - who have won all five matches so far - Rapid boast a long history in UEFA competition, having twice reached European finals in the past.
However, they have more recently been overshadowed, finishing only fourth and fifth over the past two years, and were absent from Europe entirely last term.
Now, Zoran Barisic's side can make a name for themselves by knocking out last season's Conference League finalists and securing a spot in the autumn group phase - however, there are at least 90 minutes at the inimitable Stadio Franchi to negotiate yet.
Fiorentina Europa Conference League form:
L
Fiorentina form (all competitions):
Rapid Vienna Europa Conference League form:
D
W
W
Rapid Vienna form (all competitions):
D
L
W
W
W
D
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Team News
Both Sofyan Amrabat and Luka Jovic have been left out of recent squads as they seek moves away from Fiorentina before the transfer window slides shut, and neither is set to feature on Thursday.
In addition, Antonin Barak, Gaetano Castrovilli, Abdelhamid Sabiri and Jonathan Ikone again miss out through injury.
Signed earlier this summer to replace Benfica-bound Arthur Cabral, Argentine striker Lucas Beltran made his first competitive start for the Viola against Lecce, but he must hope his performance was sufficient to hold off the claims of fellow new-boy M'Bala Nzola.
Whoever features up front should be supported from the right flank by Nicolas Gonzalez, who has scored in each of his last three league appearances: following Sunday's opening goal, all of the winger's last four Serie A strikes have been headed - none of his previous 11 were.
Rapid, meanwhile, are expected to revert to a similar XI to that which started last week's clash in Austria; first-leg scorer Marco Grull and star striker Guido Burgstaller were both dropped to the bench at the weekend.
Having recently suffered a serious injury, defender Nenad Cvetkovic will not travel to Tuscany, with Maximilian Hofmann stepping into the Serbian's shoes once again.
Incidentally, 11 Austrians were selected by coach Zoran Barisic last Thursday - including five academy graduates - and a similar number of home-grown players should stride out at Stadio Franchi.
Fiorentina possible starting lineup:
Terraciano; Dodo, Milenkovic, Ranieri, Biraghi; Duncan, Mandragora; Gonzalez, Bonaventura, Kouame; Beltran
Rapid Vienna possible starting lineup:
Hedl; Schick, Querfeld, Hofmann, Auer; Kerschbaum, Sattlberger; Oswald, Seidl, Grull; Burgstaller