The Viola led 3-1 from the first leg and dominated the first half back at the Stadio Artemio Franchi before Josip Ilicic's free-kick early in the second extended their lead.
The Danes levelled on the night through substitute Mikkel Vestergaard's late goal but were beaten 4-2 on aggregate.
Fiorentina's Borja Valero, banned for four matches domestically after being sent off against Parma and then pushing the referee, was available for this game and his corner led to the first chance, Marvin Compper shooting over.
Valero then shot wide before Ilicic's effort was saved by goalkeeper Martin Dubravka.
Compper was proving a threat from set-pieces but again missed the target in the 27th minute, heading Ilicic's corner wide.
Gonzalo Rodriguez shot over and Dubravka saved from Ryder Matos as the home side continued to dominate, still to little avail.
Esbjerg lost Jesper Rasmussen to injury four minutes before half-time, Vestergaard taking his place.
Another Valero corner in the last minute of the half led to Ilicic volleying over from range as the score remained 0-0 on the night.
There was no change to the pattern of the game upon the resumption with Fiorentina straight back on the attack, although on this occasion they managed to find the breakthrough with Ilicic curling his 47th-minute free-kick into the top corner from 25 yards.
The kick was awarded after Compper was fouled by Davidson Drobo-Ampem, who in the first leg had miscued a clearance to gift Ilicic the second goal before conceding the penalty from which Alberto Aquilani scored the third.
Matos shot wide before Esbjerg finally came to life, Casper Nielsen shooting over from long range before testing goalkeeper Antonio Rosato with an angled shot.
Another Nielsen effort went harmlessly wide before Drobo-Ampem shot over from range.
Fiorentina's Marko Bakic shot wide and Manuel Pasqual drew a superb save from the defiant Dubravka.
Nielsen, who was carrying all Esbjerg's threat, sent another long-range shot wide before Fiorentina went close through Valero and Juan Manuel Vargas.
Vestergaard gave Esbjerg the consolation of drawing the second leg with a superb solo goal in injury time, nutmegging Compper before a classy finish, but it was meaningless in the context of the tie as a whole.