Thumping their Serbian counterparts 6-0 sent the Viola into a three-way tie at the top of Group F, where they join Genk and Ferencvaros on five points.
Match preview
After drawing the opening two games of their group-stage campaign by the same 2-2 scoreline, Fiorentina entered a double-header with outsiders Cukaricki aiming for nothing less than maximum points.
Vincenzo Italiano's men welcomed the group stage debutants to Stadio Artemio Franchi two weeks ago, and after a first-half blitz they led by three goals and their visitors had been reduced to 10 men.
By the final whistle, Lucas Beltran's brace and four further strikes saw the Viola cruise to victory - and edge into Group F's top two - but they have since lost to both Lazio and Juventus in Serie A, falling into the familiar trap of chronic inconsistency.
Though Fiorentina made a strong start domestically, they have now slipped down to eighth in the table, having failed to convert a series of half-chances and fired blanks in two league fixtures last week. Losing to old foes Juve proved particularly galling, as the Turin club grimly ground out a 1-0 win in Florence despite being on the back foot throughout.
Ahead of two more tough tests, against in-form Bologna and Scudetto contenders AC Milan, Italiano will want to avoid any further slip-ups in the Conference League - a competition that Fiorentina came within a whisker of winning last season.
As Ferencvaros and Genk must play each other again, the chance now arises to cement a top-two place, before a crucial home clash with the Belgian club later this month.
Having been made to pay for inexperience during their first-ever trip to Italy in European competition - most notably, Luka Subotic receiving a red card before the break - Cukaricki remain rock-bottom of Group F and are yet to pick up a point.
After being thrashed by Olympiacos in the Europa League playoffs, Igor Matic's men have endured a tough time in UEFA third-tier tournament so far, as in addition to their six-goal reverse in Tuscany they have also lost to both Ferencvaros and Genk.
The Belgrade-based club are off the pace in the Serbian Super League too, and having only missed out on a place in Champions League qualifying on goal difference last term they now sit a distant sixth - much closer to mid-table than the top three.
Most recently, Cukaricki were beaten 2-0 by TSC Backa Topola at the weekend, although they did progress to the second round of Serbia's national cup via a penalty shootout last Wednesday.
A tally of just two 90-minute victories from their last 16 matches demonstrates their downward spiral, but even a squad low on confidence can surely find an extra gear for one of the club's most prestigious European ties to date.
Cukaricki Europa Conference League form:
L
L
L
Cukaricki form (all competitions):
L
L
L
L
L
Fiorentina Europa Conference League form:
L
W
D
D
W
Fiorentina form (all competitions):
D
W
L
W
L
L
Advert - content below:
Team News
Although he joined Fiorentina's players in holding a media blackout following Sunday night's defeat to Juventus - in protest for being made to fulfil the fixture amid fatal flooding in Tuscany - coach Vincenzo Italiano has since suggested he will rotate his squad on Thursday.
Some fringe players should be given a run-out, with a greater focus on stopping the rot in Serie A by beating Bologna at the weekend. Therefore, M'Bala Nzola may replace Lucas Beltran up front and teenage defender Pietro Comuzzo could come in at right-back, which is the Viola's current problem position: Italy Under-21 international Michael Kayode recently joined Dodo on the sidelines due to injury.
Gaetano Castrovilli is also unavailable, but Yerry Mina completed his return with a substitute appearance against Juve and should be involved again.
Meanwhile, Cukaricki's main absentee will be centre-back Luka Subotic, who must serve a suspension following his dismissal at Stadio Franchi last month. Vojin Serafimovic could replace him at the heart of the hosts' defence.
Former Partizan Belgrade winger Djordje Ivanovic has scored the Serbian side's only Group F goal so far and is set to start in attack.
Cukaricki possible starting lineup:
Belic; Rogan, Vranjes, Serafimovic, Tosic; Stankovic, Docic, Sissoko; Adzic, Adetunji, Ivanovic
Fiorentina possible starting lineup:
Terracciano; Comuzzo, Milenkovic, Ranieri, Parisi; Duncan, Lopez; Ikone, Bonaventura, Brekalo; Nzola