The London club's shock defeat to Sunderland on Saturday gave Brendan Rodgers' side the chance to open up a five-point lead at the top of the table with victory at Carrow Road.
Raheem Sterling's brace, which sandwiched a Luis Suarez strike, ensured they did just that - despite a courageous second-half fightback from the hosts.
Sterling and Suarez scored within the opening 11 minutes as Norwich failed to deal with a trademark blistering start from Liverpool.
England international Sterling picked up where he left off against Manchester City last week by firing Rodgers' men ahead early on, before Norwich's nemesis Suarez - who now has 12 goals in just five games against the Norfolk outfit - doubled the advantage soon after.
Norwich responded superbly after the interval and Gary Hooper's first league goal since Boxing Day reduced the arrears.
Sterling was on hand to settle any Liverpool nerves just after the hour with his second goal, although they were then forced to endure a nervy final 13 minutes after Robert Snodgrass nodded home Martin Olsson's cross.
Liverpool's 11th Premier League win in a row - a new club record - puts them firmly in the driving seat for a first top-flight title since 1990, while Norwich remain just two points above the relegation zone.
Joe Allen and Lucas Leiva came in for Daniel Sturridge and Jordan Henderson, absent through injury and suspension, with Sterling reprising his role at the tip of a midfield diamond that caused City so many problems last week.
Just as he did against Manuel Pellegrini's team, the in-form teenager gave Liverpool an ideal start by breaking the deadlock in stunning fashion after four minutes.
Philippe Coutinho fed Sterling, who dipped inside and drove an unstoppable shot past the helpless John Ruddy, with the aid of a slight deflection off Michael Turner, from 25 yards.
The visitors were playing with a verve and swagger that has often been evident during their fantastic run of form, and Allen forced Ruddy into a fine save before Suarez, inevitably, got on the scoresheet with his 30th Premier League goal of the season.
Jon Flanagan fed Sterling down the left and he rolled a weighted ball across the face of goal for Suarez, who evaded Turner before calmly side-footing past Ruddy from eight yards.
Norwich responded admirably and Hooper was only denied what looked a certain goal by Allen's last-ditch intervention in the area.
Having started the second half on the front foot, Norwich got back into the game nine minutes after the restart when Liverpool goalkeeper Simon Mignolet made a mess of a cross under pressure from Bradley Johnson and Hooper was on hand to finish from close range.
Sterling quickly restored the visitors' two-goal cushion, as he capitalised on Johnson's wayward pass to run at the heart of the Norwich defence, before eventually beating Ruddy with a left-footed shot that took a wicked deflection off the retreating Johnson.
Snodgrass' header 13 minutes from time gave a spirited Norwich side an unlikely glimmer of hope, but Liverpool held on for a crucial three points as Mignolet kept out a late header from substitute Ricky van Wolfswinkel.
