Sadio Mané made a triumphant return from injury as he came off the bench to net a 78th-minute winner for the Reds at Carrow Road, sending the leaders 25 points clear at the top of the Premier League with a game in hand, after their 17th successive league victory.
Facing an unchanged Canaries outfit, Jürgen Klopp opted for a single alteration from the 4-0 victory over Southampton, with Naby Keïta, making his first start since returning from injury, replacing Fabinho.
Trent Alexander-Arnold and Alex Oxlade-Chamberlain fired wide and forced a comfortable save out of Tim Krul respectively in the opening 10 minutes of a quiet opening half-an-hour.
The only other moment of note in the opening 30 saw Sam Byram forced off with what looked a hamstring strain, with Jamal Lewis replacing him in the 27th minute.
From there, things began to get a bit livelier.
Andrew Robertson got in-behind in the 33rd minute but saw a low cross well intercepted by fellow Scot, Grant Hanley, and Naby Keïta scuffed a volley wide from 25-yards.
The hosts then had their clearest opening, as Lukas Rupp latched onto a flighted pass in-behind the high Liverpool line. The German looked to square to Teemu Pukki but Alisson Becker did superbly to read it and stretch out a glove to intercept.
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Replays did suggest the German may have been penalised for offside via VAR had a goal been scored but it was encouragement for Norwich nonetheless.
It proved the last significant action of the opening 45.
The Reds looked more proactive early in the second, with Robertson flashing a low delivery across the six-yard box and Keïta seeing a powerful 25-yard drive tipped over in its opening 13 minutes.
Then came their first really clear chance, but Krul’s superb double save denied them, as he first kept out Mohamed Salah’s low right-footed shot before smothering Keïta’s rebound in the 59th minute.
Shortly after that, Mané, along with Fabinho, was introduced.
Alexander Tettey hit the near-post with a clever attempt from range in the 72nd minute, but the Senegalese would prove the difference.
With a little over 12 minutes of normal time remaining, Jordan Henderson found space a few yards inside the Norwich half before looking up and delivering a familiarly accurate diagonal ball.
Mané ushered away Christoph Zimmermann — an action that was subject to a VAR check before he controlled on his chest, swivelled a lashed a superb left-footed finish into the bottom-left corner.
There could have been more. Roberto Firmino would fire an Alexander-Arnold cross wide from point-blank range in the 86th minute, while Pukki could only find the gloves of Alisson when he was released three minutes later.
That moment of late quality from the 27-year-old would prove the difference though and earn the league leaders yet another hard-fought win.