Proudly unbeaten in their last six matches across all competitions (W4, D2), Fiorentina started the game the better of the two sides here, and went close to taking the lead after just 11 minutes, when Marin Pongracic was found free inside the penalty area from a corner, but the Croatian sent his header over the crossbar.
Celje grew into the game as the first half went on, though, and they very nearly brought the tie level midway through the first half, with Tamar Svetlin firing towards the bottom-right corner from inside the penalty area, only to be denied by the heroics of David De Gea.
The best chance for the hosts inside the opening half-hour came after 28 minutes, when Nicolo Fagioli found Rolando Mandragora with an exquisite chipped pass, but he saw his header stopped by a phenomenal reflex save from Ricardo Silva.
However, Fiorentina did eventually manage to break the deadlock, with Mandragora getting his name on the scoresheet. Instinctively latching onto a precise pass from Pongracic, he kept his cool and slotted the ball into the bottom-left corner past a helpless Ricardo Silva.
The start to the second half wasn’t as easy as Fiorentina would've liked, with Celje equalising in the 54th minute after Aljosa Matko raced on to Mark Zabukovnik’s through ball before calmly slotting a cool finish into the bottom-right corner.
And the tie was well and truly back in the balance with 66 minutes on the clock, as Celje took the lead when Klemen Nemanic put an unbelievable header into the top-left corner.
Albert Riera’s side's joy was short-lived lived though, with Fiorentina taking the lead again just a minute later, after some fantastic work from Moise Kean saw the forward bend a lovely strike into the far bottom-right corner.
There would be no continuation to the fairytale of Celje - the only Slovenian side ever to reach the final eight of a major European tournament. Instead, La Viola managed to see the game out from there to secure a place in the semi-finals, leaving Fiorentina unbeaten in 12 two-legged UEFA Conference League ties.
Flashscore Man of the Match: Rolando Mandragora (Fiorentina)