Harvey Elliott marked his return from injury with his first Liverpool goal as Jurgen Klopp's side beat Cardiff 3-1 at Anfield to set up a FA Cup fifth-round tie against Norwich.
Elliott, who had not featured at all since dislocating his ankle during a Premier League meeting with Leeds in September, controlled an Andrew Robertson cross and fired a clinical finish into the corner (76) after coming off the bench in the second half.
Elliott later described the goal as a moment he will "cherish forever" while Klopp added: "He was patient coming back and he's still a fearless boy and a great footballer. Getting this goal was a really touching moment."
Earlier, Diogo Jota had put the hosts in front with a superb header from Trent Alexander-Arnold's free-kick (53), before Takumi Minamino doubled Liverpool's advantage from a cut-back by new signing Luis Diaz (68), the substitute marking his debut with an assist.
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Cardiff did give their fans something to cheer after that, with teenage substitute Rubin Colwill firing past Liverpool goalkeeper Caoimhin Kelleher after exchanging passes with Isaak Davies (80), but the Championship side were well beaten in the end as Liverpool advanced to the fifth round for only the second time under Klopp.
It might have been a different story had the visitors been able to build on a resilient first-half performance during which they frustrated a Liverpool side still missing Sadio Mane and Mohamed Salah at the Africa Cup of Nations.
Jota would eventually take his tally for the season to 15 goals, but he missed a gilt-edged chance inside the first few minutes when he shot too close to Cardiff goalkeeper Dillon Phillips after creating space for himself with a brilliant turn.
It set the tone for a wasteful first-half showing, with Curtis Jones, Roberto Firmino and Naby Keita also spurning opportunities as Liverpool reached the halfway point having had 10 shots but only one on target.
Cardiff saw little of the ball but did threaten on occasion, not least when Mark Harris saw a penalty appeal turned down - the decision upheld by VAR - after going to ground under pressure from Ibrahima Konate in the Liverpool box.
The VAR was called into action again moments after the break when Kelleher, starting in place of Alisson Becker, raced off his line in an attempt to make a clearance but ended up bringing down Harris.
The young goalkeeper appeared to have his studs up as he challenged Harris but a yellow card was deemed sufficient.
Jota's outstanding opener, when he directed Alexander-Arnold's delivery into the far corner from 12 yards out, arrived soon afterwards.
The Portuguese international then volleyed narrowly wide from a corner but Liverpool didn't have to wait long for their second goal when Diaz, whose introduction was met with raucous cheers by the home fans, won possession off a dawdling Perry Ng to set up the onrushing Minamino.
There was subsequently a worrying moment for the Colombian international, a January arrival from Porto, when he went down in pain and needed treatment following a coming together with a Cardiff player, but while the collision left him with a cut on his knee, he was able to continue.
Elliott's strike completed a satisfying afternoon's work for Liverpool, for whom Kostas Tsimikas was particularly impressive at left-back, although the travelling Cardiff fans also experienced a moment to savour when 19-year-old Welsh international Colwill fired home their consolation goal.
Elliott: Goal a moment to cherish forever
Goalscorer Harvey Elliott expressed his delight afterwards, telling ITV Sport: "It's hard to put into words at the moment. It's what I've been put into the team to do - to score and assist. Thankfully, it's come today in front of the fans after a long time out.
"It's my job, and I just have to keep doing it. It's a moment that for myself and for my family we will cherish forever."
On his goal, he added: "It wasn't too bad. Watching Diogo next to me, I've been getting tips off him!"
Th 18-year-old also paid tribute to Liverpool physio Joe Lewis for helping him through his injury rehabilitation.
"One man I have to thank is Joe," he said. "He's one of the physios who took me in during the early hours of the morning and we didn't finish until late at night. He made me strong again.
"A big shout out to all of my friends and family as well, especially my mum and dad. They've supported me throughout. A massive thanks to the fans who gave me all the love. The injury is behind me now and I'm back."
Klopp hails Elliott comeback as Diaz gets English welcome
Asked about Harvey Elliott afterwards, Jurgen Klopp told ITV Sport: "He was unlucky with the injury but then lucky with the whole process afterwards.
"Everything has gone well. He did an incredible job and the medical department did an incredible job.
"He was patient coming back and he's still a fearless boy and a great footballer. There are not a lot of good things when you get an injury like that, but when you are that young, you deal with it better.
"Getting this goal was a really touching moment."
Luis Diaz, meanwhile, enjoyed a promising debut from the bench as he set up Liverpool's second goal but he also needed treatment after a Cardiff boot landed on his knee in the closing stages.
Klopp added: "Luis came on and it's just a little bruise, a little cut. Everyone in the dressing room said, 'Welcome to England'. That will be a scar in the end from his first game, but it's all good."
FA Cup fifth round draw in full
- Luton Town vs Chelsea
- Crystal Palace vs Stoke City
- Peterborough United vs Manchester City
- Liverpool vs Norwich
- Southampton vs West Ham
- Middlesbrough vs Tottenham Hotspur
- Nottingham Forest vs Huddersfield Town
- Everton vs Bournemouth or Boreham Wood
The ties will be played in the week commencing Monday February 28, 2022.
What's next for Liverpool and Cardiff?
Liverpool host Leicester City in the Premier League on Thursday at Anfield at 7.45pm while Cardiff return to Championship action at home to Peterborough on Wednesday at 7.45pm, live on Sky Sports Football via the red button.