Brendan Rodgers side were beaten on home soil by their Italian opponents in a game that came to life in the final half an hour, despite appearing comfortable in the opening period
The hosts took the lead in a first half in which they largely out-played their illustrious visitors, with Jonjo Shelvey nodding home inside the box after a decent ball back into the box by Stewart Downing.
But Udinese came out of the traps a different side in the second half, and they equalised just 32 seconds after the break through a delightful curled finish from Antonio Di Natale.
They continued their comeback with two goals in quick succession through a Sebastian Coates own goal and a crisply hit strike from outside the box by Giovanni Pasquale before Luis Suarez grabbed one back shortly after with a marvellous free-kick.
Liverpool boss Brendan Rodgers rang the changes for the fixture, drafting in eight players left out of the 5-2 away win over Norwich at the weekend. Jamie Carragher, Jack Robinson and Sebastian Coates came in for Andre Wisdom, Daniel Agger and Martin Skrtel at the back.
In midfield, Shelvey and Jordan Henderson were brought in for Steven Gerrard and Nuri Sahin, while Rodgers also named a completely changed front three, with Fabio Borini, Oussame Assaidi and Downing handed starts.
Franceso Guidolin had a full-strength side to choose from as Udinese looked to put their slow start to the new league season behind them, with star striker Di Natale restored to the starting line-up after being dropped for their clash at the weekend against Genoa.
With Liverpool dominating possession in the initial stages, the first clear-cut chance of the half came until the seventh minute when Coates went close with a point-blank header from a corner, only to see Zeljko Brkic pull out a good low stop.
Udinese went close to taking the lead in the 13th minute but were denied by a magnificent save by Pepe Reina, who got down low to his right to keep out a firm Mehdi Benatia header from a Di Natale free-kick wide on the right.
With the game beginning to open up, Borini went close moments later after wriggling clear of two Udinese defenders before firing just wide of the bottom right-hand post.
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Liverpool were beginning to knock the ball around with confidence and almost doubled their tally through a Henderson header after a lovely flowing move, with Udinese reduced to hitting on the break with only a speculative strike from Di Natale to show for their efforts, and the Reds led at the break.
However, after a lacklustre first half, an incisive move saw winger Andrea Lazzari arrow a low cross in for Di Natale to take first time with the ball rolling across his body, arching his curled effort brilliantly into the top right-hand corner past the despairing Reina to grab an equaliser in the first minute of the second half.
With both sides struggling to keep hold of the ball and cancelling each other out, it took a double substitution from Rodgers, bringing on both Suarez and Steven Gerrard, to bring his side back to life.
After Downing burst down the right, Giampiero Pinzi's absurd rugby tackle led to Suarez going close with a chance from the resulting free-kick, only to see his sweetly struck effort cleared off the line unwittingly by Shelvey trying to poke the ball home at the back post.
They were made to pay for that miss moments later, when Coates nodded into his own net under pressure from Maurizio Domizzi after a dangerous free-kick from Lazzari into the box in the 70th minute.
With Liverpool now needing a goal to get back into a game they had looked comfortable in for large periods, they were caught on the break when Di Natale, who was instrumental throughout, brought down a long punt forward brilliantly in the 73rd minute before laying the ball off to Pasquale to drive into the bottom right corner from outside the box to complete a dramatic turnaround.
This seemed to bring the hosts back to life and Suarez stepped up to strike a fantastic free-kick into the top-left corner from just outside the area in the 75th minute to set up a tense finish.
They should have drawn level moments later when Suarez was denied by a Brkic save after a fabulous cross from Downing on the right, with the Uruguayan aiming his free header right at the goalkeeper before the Udinese defence scrambled the ball away.
With Udinese standing off more and more and inviting the hosts' late pressure, Suarez went close and substitute Raheem Sterling twice nearly guided efforts into the top corner as Liverpool flooded forward in the pursuit of a dramatic late equaliser.
The final chance of the game fell to the lively Downing, but his drive was straight at Brkic and Udinese held on to clinch a real smash-and-grab victory while for Liverpool, it was yet another in a long line of results which simply did not match their impressive performance.