Jordan Henderson scored his first European goal as Liverpool beat Udinese to reach the Europa League last 32.
Henderson's low strike midway through the first half ensured the Reds finished top of Group A and qualified alongside Russians Anzhi Makhachkala.
Luis Suarez twice went close to doubling Liverpool's lead in Italy, with Henderson denied a second.
Udinese had Giovanni Pasquale sent off while Antonio Di Natale fired just over the bar with the last kick of the game.
It was a glorious opportunity and would have knocked Liverpool out had it found the back of Pepe Reina's net.
Solid at the back
Liverpool have now kept clean sheets in five of their last six visits to Italy in European competition
The Reds were able to breathe a huge sigh of relief and can now look forward to the draw for the knockout stage on 20 December.
They arrived in Italy knowing victory offered the only guarantee of progress and Brendan Rodgers named a strong line-up that produced a display combining attacking enterprise with defensive resilience.
Luis Suarez started his first European away match for the club and troubled the Udinese defence throughout, while Jamie Carragher and Martin Skrtel formed an uncompromising centre-back partnership.
Suarez linked effectively with Suso and Henderson from the right, and Stewart Downing and Jose Enrique from the left, as well as with Jonjo Shelvey after he replaced the injured Nuri Sahin early on.
Nevertheless, it was Udinese who threatened first, Mathias Ranegie heading wide and Reina tipping Roberto Pereyra's shot over the bar.
But Liverpool were racing forward in numbers at every opportunity, passing and moving quickly and precisely to expose the hosts.
One such move helped earn them a corner and after Downing's set-piece found its way to Henderson via Suarez and Suso, the 22-year-old drilled a low finish through the legs of Daniele Padelli.
Udinese were still coming to terms with the setback when Liverpool almost struck again, Glen Johnson's close-range strike disallowed after Downing crossed from an offside position.
Diego Fabbrini tested Reina as Udinese looked to reply, yet the lack of confidence that comes with three straight European defeats was clear and Liverpool's well-organised back line stood firm.
Suarez went close with an overhead kick as Liverpool finished the half well and although home coach Francesco Guidolin made a change at the break, he resisted the temptation to introduce Di Natale.
Instead, Medhi Benatia came on and even when he had to go off injured, debutant Max Reinthaler was preferred to the veteran striker.
Udinese did threaten an equaliser when Ranegie headed just over the bar from Pasquale's corner, while at the other end Padelli made a fine save from Henderson's volley and an even better one to deny Suarez.
The Italians lost Pasquale to a second booking but it failed to halt the late momentum and they pushed hard for an equaliser.
Di Natale was finally introduced on 85 minutes and almost stole the show, only to lash over the bar from a superb position.
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Live Text Commentary
Full Time The final whistle is blown by the referee.90:00 +3:11
Antonio Di Natale produces a right-footed shot from deep inside the penalty area which goes wide of the right-hand post.90:00 +2:25
Sanchez Jose Enrique challenges Diego Fabbrini unfairly and gives away a free kick. Max Reinthaler takes the direct free kick.90:00 +1:59
Raheem Sterling concedes a free kick for a foul on Larangera Danilo. Free kick taken by Daniele Padelli.89:53
Corner taken short by Joe Allen.87:29
Free kick awarded for a foul by Pablo Armero on Raheem Sterling. Direct free kick taken by Glen Johnson.86:40
Thomas Heurtaux gives away a free kick for an unfair challenge on Luis Suarez. Jonjo Shelvey takes the free kick.86:01
Foul by Max Reinthaler on Jordan Henderson, free kick awarded. Martin Skrtel takes the free kick.84:50 Substitution
Substitution Antonio Di Natale on for Math Ranegie.82:49
Martin Skrtel challenges Math Ranegie unfairly and gives away a free kick. Pablo Armero takes the direct free kick.81:03
Emmanuel Agyemang-Badu takes the free kick.81:03 Booking
Booking Jamie Carragher is shown a yellow card.80:59
Jamie Carragher challenges Diego Fabbrini unfairly and gives away a free kick.80:15
Corner taken right-footed by Jonjo Shelvey, save by Daniele Padelli.79:25 Booking
Booking Emmanuel Agyemang-Badu is shown a yellow card for dissent.79:03 Dismissal
Dismissal Giovanni Pasquale is shown a red card.78:30
Free kick awarded for an unfair challenge on Raheem Sterling by Giovanni Pasquale. Direct free kick taken by Stewart Downing.75:24
Corner taken left-footed by Roberto Pereyra, Math Ranegie has a headed effort at goal from deep inside the area missing to the left of the target.74:29
Martin Skrtel challenges Emmanuel Agyemang-Badu unfairly and gives away a free kick. Direct free kick taken by Giovanni Pasquale.71:37
Unfair challenge on Roberto Pereyra by Raheem Sterling results in a free kick. Free kick taken by Giovanni Pasquale.
Direct free kick taken by Emmanuel Agyemang-Badu.70:02 Substitution
Substitution Jesus Fernandez Saez goes off and Raheem Sterling comes on.70:02 Booking
Booking Joe Allen shown a yellow card.69:55
Joe Allen challenges Diego Fabbrini unfairly and gives away a free kick.68:42
Free kick awarded for an unfair challenge on Jesus Fernandez Saez by Giovanni Pasquale. Glen Johnson restarts play with the free kick.67:19
Luis Suarez takes a shot. Save by Daniele Padelli. Outswinging corner taken by Sanchez Jose Enrique.66:26
Glen Johnson takes the direct free kick.66:26 Booking
Booking Giovanni Pasquale booked for unsporting behaviour.66:19
Giovanni Pasquale gives away a free kick for an unfair challenge on Jesus Fernandez Saez.64:15
Save by Daniele Padelli. Corner taken by Jonjo Shelvey, save by Daniele Padelli.64:15 Substitution
Substitution (Udinese) makes a substitution, with Max Reinthaler coming on for Mehdi Benatia.64:15
Jordan Henderson takes a shot.61:22
Free kick awarded for a foul by Giovanni Pasquale on Luis Suarez. Martin Skrtel takes the free kick.59:06
The ball is delivered by Pablo Armero, clearance by Martin Skrtel. Corner taken by Davide Faraoni, Headed effort from deep inside the penalty area by Math Ranegie goes harmlessly over the crossbar.58:38
Jamie Carragher challenges Math Ranegie unfairly and gives away a free kick. Direct free kick taken by Larangera Danilo.57:09
Mehdi Benatia concedes a free kick for a foul on Luis Suarez. Glen Johnson takes the direct free kick.55:26
Outswinging corner taken right-footed by Jonjo Shelvey from the right by-line, Larangera Danilo manages to make a clearance.53:37
Emmanuel Agyemang-Badu produces a right-footed shot from long range which goes wide right of the goal.51:19
Pablo Armero takes a shot. Martin Skrtel gets a block in. Outswinging corner taken by Davide Faraoni from the right by-line.49:08
Luis Suarez takes a shot from just outside the penalty area which clears the crossbar.48:08
Sanchez Jose Enrique is penalised for a handball. Direct free kick taken by Davide Faraoni.46:48
Effort from inside the area by Jesus Fernandez Saez misses to the right of the target.45:01
The game restarts for the second half.45:01 Substitution
Substitution Giampiero Pinzi goes off and Mehdi Benatia comes on.45:00 +1:47 Half time
Half Time The whistle is blown to end the first half.45:00 +0:31
Corner taken by Jonjo Shelvey. Shot by Luis Suarez from 6 yards. Save made by Daniele Padelli.43:45
Shot by Luis Suarez from deep inside the penalty area misses to the right of the goal.43:18
Luis Suarez gives away a free kick for an unfair challenge on Larangera Danilo. Direct free kick taken by Larangera Danilo.40:53
Outswinging corner taken from the right by-line by Jonjo Shelvey, clearance made by Larangera Danilo. A cross is delivered by Jonjo Shelvey, Headed effort from deep inside the penalty area by Jesus Fernandez Saez goes harmlessly over the crossbar.38:34
Sanchez Jose Enrique delivers the ball, save by Daniele Padelli.38:09
Giampiero Pinzi takes a shot. Save made by Jose Reina.37:50
Pablo Armero fouled by Jordan Henderson, the ref awards a free kick. Free kick taken by Giampiero Pinzi.35:44
Larangera Danilo restarts play with the free kick.35:44 Booking
Booking Jesus Fernandez Saez is shown a yellow card for unsporting behaviour.35:05
Free kick awarded for a foul by Jonjo Shelvey on Roberto Pereyra.33:11
Diego Fabbrini takes a shot. Jose Reina makes a save.32:43
The assistant referee signals for offside against Luis Suarez. Larangera Danilo takes the indirect free kick.31:16
Martin Skrtel concedes a free kick for a foul on Math Ranegie. Giampiero Pinzi restarts play with the free kick.30:34
Jamie Carragher fouled by Math Ranegie, the ref awards a free kick. Jose Reina takes the free kick.29:03
Diego Fabbrini fouled by Stewart Downing, the ref awards a free kick. Emmanuel Agyemang-Badu restarts play with the free kick.27:39
Free kick awarded for a foul by Luis Suarez on Larangera Danilo. Free kick taken by Giampiero Pinzi.26:15
The referee blows for offside. Daniele Padelli takes the indirect free kick.22:45
Assist on the goal came from Jesus Fernandez Saez.22:45 Goal scored
Goal! - Jordan Henderson - Udinese 0 - 1 Liverpool Jordan Henderson finds the back of the net with a goal from deep inside the penalty box to the bottom left corner of the goal. Udinese 0-1 Liverpool.22:16
Outswinging corner taken by Stewart Downing.21:07
Free kick awarded for an unfair challenge on Jonjo Shelvey by Giampiero Pinzi. Luis Suarez takes the free kick.20:27
Free kick awarded for a foul by Giovanni Pasquale on Jesus Fernandez Saez. Glen Johnson takes the direct free kick.18:53
Roberto Pereyra takes a shot. Jose Reina makes a save. Outswinging corner taken left-footed by Giovanni Pasquale played to the near post.17:41
Corner from the right by-line taken by Davide Faraoni, Stewart Downing makes a clearance.16:35
Jordan Henderson restarts play with the free kick.16:35 Booking
Booking Diego Fabbrini is shown a yellow card.16:31
Foul by Diego Fabbrini on Jonjo Shelvey, free kick awarded.15:03
The ball is swung over by Giovanni Pasquale, Headed effort from deep inside the penalty area by Math Ranegie misses to the right of the target.14:35
Jesus Fernandez Saez takes a shot. Save made by Daniele Padelli.11:50
Shot by Jonjo Shelvey from deep inside the penalty area misses to the left of the goal.11:04
Stewart Downing takes the direct free kick.11:04 Substitution
Substitution Jonjo Shelvey replaces Nuri Sahin.11:04
Sanchez Jose Enrique fouled by Davide Faraoni, the ref awards a free kick.4:45
Inswinging corner taken left-footed by Nuri Sahin from the right by-line, save by Daniele Padelli.3:21
Unfair challenge on Jesus Fernandez Saez by Pablo Armero results in a free kick. Glen Johnson restarts play with the free kick.1:00
Math Ranegie concedes a free kick for a foul on Martin Skrtel. Jose Reina takes the direct free kick.0:13
Outswinging corner taken from the right by-line by Giampiero Pinzi.0:00
The match gets underway.
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