Fiorentina had already done the work, so this 1-1 draw with Esbjerg set up the Europa League showdown with Juventus.
The Viola had already won the first leg 3-1 in Denmark, so were able to make a few changes, including Antonio Rosati in goal. Ryder Matos played on his 21st birthday and Mario Gomez got his first start since damaging knee ligaments in September, while Borja Valero was picked ahead of his four-match Serie A ban.
It felt more like a training exercise than a Europa League knockout tie with a low tempo and very little happening. Josip Ilicic had an early shot deflected and Marvin Compper ballooned over from a corner.
Another Compper header skimmed the upright from a set piece and David Pizarro’s screamer had more power than accuracy, whistling wide of the woodwork. Esbjerg lost Rasmussen to an injury before half-time.
Fiorentina finally broke the deadlock straight after the restart with Ilicic curling a free kick over the wall and into the near top corner.
However, Vestergaard managed to shake off Compper in the box and forced a tough save out of Antonio Rosati from close range.
Ilicic’s strike was deflected over the bar and Gomez had scored when dribbling round the goalkeeper to deposit into the net from a tight angle, but the goal was ruled offside in an incredibly tight decision.
Marko Bakic almost scored another for the Viola, but his chip shaved a coat of paint off the frame of the goal.
Pizarro set up Manuel Pasqual for a first-time finish that forced Dubravka into a save. Esbjerg also had some chances late on, as Rosati had to rush off his line to clear from Vestergaard, then Nielsen drilled inches past the base of the far post.
Borja Valero went for goal from distance and his thunderbolt was beaten away with some difficulty.
Esbjerg earned a consolation goal in stoppages when Vestergaard shimmied past Compper to flash his shot across Rosati into the far top corner.
Bakic almost restored the victory, but again was narrowly off target.
Fiorentina dominated this tie and will now face their arch-rivals Juventus in the Round of 16.
Fiorentina 1-1 Esbjerg (4-2 on agg)
Scorers: Ilicic 47 (F), Vestergaard 91 (E)
Fiorentina: Rosati; Roncaglia, Gonzalo Rodriguez (Tomovic 60), Compper, Pasqual (Vargas 78); Ambrosini (Bakic 65), Pizarro, Borja Valero; Ilicic, Gomez, Matos
Esbjerg: Dubravka; Laursen, Lucena, Drobo-Ampem, Knudsen; Rasmussen (Vestergaard 42), Bergvold, J Andersen (Levken 68), Nielsen; Pusic (J Ankersen 57); Van Buren
Ref: Strahonja (CRO)