Three goals in 15 minutes made for a frantic first half at the Blue Water Arena, but the former Liverpool midfielder's penalty secured a two-goal win for the visitors
On-loan AC Milan man Alessandro Matri showed solid skill to score the opener but Danish forward Martin Pusic equalised a minute later, after the Viola failed to clear a dangerous cross.
Five minutes later, though, Josip Ilicic cooled the visiting fans' nerves and Alberto Aquilani effectively killed off the tie with a penalty shortly before half-time.
Vicenzo Montella's men saw out the second half with little fuss to leave them with a considerable advantage heading into the second leg at the Stadio Artemio Franchi.
German striker and summer signing Mario Gomez was on the bench once again for Fiorentina, having made his comeback from a long spell out injured as a substitute at the weekend.
Pusic will have made Montella question how soon he might need a forward like Gomez on the pitch as he tested Viola shot-stopper Neto with four minutes gone.
But it was the visitors who got the goalscoring under way. Matri, on a half-season loan from Milan, controlled a pass perfectly before then burying his effort in the bottom corner.
Before Fiorentina even had a chance to settle following the celebrations, Pusic pounced on a deep cross to fire Esbjerg level with a low and accurate strike.
A breathless opening 15 minutes ended with Ilicic scoring from a threatening cross curled into the box.
The tempo died down in the subsequent five minutes and the next chance came with a third of the game gone, as Esbjerg midfielder Markus Levken's cross narrowly avoided causing havoc and instead went out for a corner.
Just as the hosts were starting to rediscover their verve - with Peter Ankersen's deflected effort just going wide of the post - Davidson Drobo Ampem brought down Ryder Matos just inside the area to concede a penalty.
Esbjerg's players protested the foul was outside the box to no avail and ex-Liverpool midfielder Aquilani hit home to give the visitors a comfortable cushion.
Half-time came and went without further major incident, with Gomez's arrival on the pitch for goalscorer Matri spicing up Montella's tactics.
The former Bayern Munich forward very nearly made an instant impact upon his introduction, forcing a save from Martin Dubravka with a shot from the edge of the 18-yard box.
As the second half wound down to its predictable conclusion, Borja Valero should really have given Fiorentina an additional away goal but he screwed a rebounded Ilicic shot over the crossbar, wasting all of Matos' excellent work in creating the chance.
It did not matter with regards to the result, however, and Montella's men can consider themselves as having one foot in the final after an impressive display at the Blue Water Arena.