Udinese progressed to the last four of the competition with wins over both Milan clubs and have claimed an advantage in their two-legged semi-final.
Despite Fiorentina dominating large periods of last Tuesday's first meeting at Stadio Friuli and creating more goal-scoring opportunities, the hosts completed a smash-and-grab win late on, aiding their bid to reach the Coppa Italia final for the first time since its opening year in 1922.
Antonio Di Natale's 36th-minute opener was cancelled out just before the break by Juan Manuel Vargas, whose goal gives Fiorentina a lifeline going into the second leg, but Luis Muriel netted Udinese's winner eight minutes from time.
Colombia international Muriel has only managed to score three times in Serie A this season, but his goal against Fiorentina was his second in as many Coppa Italia matches after he also found the net in the 2-1 quarter-final win over Milan.
Fiorentina, who beat Chievo and Siena on their way to the semis, knocked out Udinese at the last-16 stage of the competition last season, but since then this fixture has had only one outcome.
Including their first-leg glory, Udinese have emerged as victors in their last three meetings with Fiorentina, although each of those games took place in Udine.
Vincenzo Montella's men go into the tie on the back of a 2-0 home win over Atalanta, secured through goals from Josip Ilicic and Rafal Wolski.
That triumph ended a run of three games without a win, keeping Fiorentina three points behind third-placed Napoli in Serie A.
By contrast, Udinese are currently enduring a disappointing season and sit way down in 14th, although they have won four of their last five games in all competitions.
Udinese coach Francesco Guidolin believes his side are approaching their best form following Saturday's 3-0 triumph over Chievo, but expects his men to continue improving.
Guidolin told Sky Italia: "We knew that we were having difficulties (against Chievo), but we remained calm.
"During the second half we increased our playing pace, acted more lively and pushed higher up the pitch. After the first goal, everything became easier. I give my compliments to Chievo, I just think our advantage became a little too heavy for them.
"I hope that the team continues like this, as now we're showing our true qualities. We must keep pushing and not let up even a little. We want to improve in this league that has now become more beautiful."
Guidolin could call upon Allan, Giampiero Pinzi and Danilo following their respective suspensions, while Zeljko Brkic remains a doubt with a back strain.
Massimo Ambrosini and Alberto Aquilani are not certain to be involved for Fiorentina due to minor knocks, but Mario Gomez could potentially be named on the bench after five months out with a knee injury.
