The Reds deservedly led at halftime thanks to a well-worked Jonjo Shelvey goal, but the Italian side levelled straight after the interval through Antonio Di Natale.
Two goals in two minutes — an own goal by Sebastian Coates and a classy strike from Giovanni Pasquale — then put the visitors well ahead.
Substitute Luis Suarez led a late effort to earn a point with a memorable free-kick, but it was Udinese who claimed the win.
A youthful Liverpool side got its Group A campaign off to a winning start against Young Boys two weeks ago — but on Thursday Brendan Rodgers selected several of the senior players likely to play against Stoke this weekend. Glen Johnson, Pepe Reina and Joe Allen started, while Steven Gerrard, Suarez, Martin Skrtel and Raheem Sterling were named among the substitutes.
It doesn't seem to matter who the personnel are for Liverpool these days, the brand of football is identical: zig-zags of short passes are used to penetrate the opposition, and so they began here.
In the first eight minutes the Udinese goal had been threatened by Oussama Assaidi following a dart into the box, Shelvey with a shot from range and Coates with a header that he should have directed beyond Zeljko Brkic.
Both sides pressed hard, and that made for a lively opening, with Udinese clearly not arriving at Anfield to sit back. In the 14th minute, Reina had to be at his very best to stop a Medhi Benatia header breaching the Kop goal. His low, reflex save was one for the scrapbook.
Shelvey's red card against Manchester United will rule him out for another domestic game yet, but he was eligible Thursday, and it was he who opened the scoring in the 23rd minute, following a slick passing move.
Jordan Henderson found his England U-21 teammate, who fed Stewart Downing before surging into the box to head the subsequent cross into the bottom corner. It was Gerrard-esque, and the youngster let out some of the frustration he obviously felt at his spell on the sidelines with an enthusiastic celebration.
As the half progressed, Udinese found themselves increasingly starved of possession, but within 30 seconds of the restart the scores were level as the visitors played Liverpool at its own game. Udinese weaved the ball beautifully through the home defence and when half-time substitute Andrea Lazzari's cross came in, Di Natale had timed his run perfectly to finish beyond Reina from 12 yards.
Liverpool's response wasn't emphatic. In the 61st minute, Downing drove himself into the box and tried a one-two with Fabio Borini. The final pass got caught underneath the Englishman's feet. Seconds later Henderson had a low shot blocked.
Rodgers decided to act, replacing Assaidi and Henderson with Gerrard and Suarez for the final 25 minutes.
The lively Downing looked to instigate another opportunity with a run down the left, outpacing his man only to be comically grappled to the floor. A red card wouldn't have been unwarranted. Instead Giampiero Pinzi received a yellow and was swiftly substituted.
Suarez collected possession from the resulting free-kick, directing a shot goalwards only to see it blocked by Shelvey.
Then, in two crazy minutes, the Reds were ambushed. First in the 70th minute, when the otherwise superb Coates headed a Udinese free-kick past his own goalkeeper, then when Pasquale thumped beyond Reina from outside the box. Anfield was hushed.
Game over? Maybe not. In the 75th minute, Liverpool were awarded a free-kick of their own, 25 yards from goal, Suarez territory. The Uruguayan found the top corner, the Kop went wild. 3-2.
Soon after Suarez had a header saved at close range, and then, after whizzing past his marker, was denied at the near post.
Substitute Sterling saw a shot from 12 yards ricochet over as the Reds threw everything at the Italians.
The 17-year-old had the final chance of the game, demonstrating all his trickery before looping over the crossbar.
Liverpoolfc.com journalists' man of the match: Joe Allen.