Esbjerg striker Martin Pusic cancelled out Alessandro Matri's opener in the 10th minute but Josip Ilicic put the Italians back in front soon after.
Alberto Aquilani wrapped up the win before half-time after converting his team's third from the penalty spot.
The Italians, fourth in Serie A, went into the encounter in Denmark as heavy favourites.
They took an eighth-minute lead when an unmarked Matri surged inside the area and slotted the ball into the net.
The hosts replied soon after when Fiorentina's defence failed to clear a dangerous cross from the right leaving Pusic to fire a six-yard shot past rival goalkeeper Norberto Neto.
The visitors retook the lead five minutes later when Davidson Drobo-Ampem's poor clearance in his area proved an assist for Ilicic and the Slovenian midfielder chested the ball down before hitting a 12-yard effort past Esbjerg goalkeeper Martin Dubravka.
Fiorentina extended their advantage in the 37th minute after being awarded a penalty, the referee pointing to the spot after Drobo-Ampem brought down in the area Santos Ryder.
Aquilani made no mistake and struck his spot-kick into the top right corner of the net, out of Dubravka's reach.
Mario Gomez replaced Matri early in the second half and the German forward saw his bullet strike kept out by Dubravka before the hour mark.
Esbjerg had their chances to put themselves back in the tie but Neto produced great saves late in the game, first from susbstitute Jesper Rasmussen and then from Pusic.
The Danes travel to Florence for the return leg on February 27.