Manchester City had overtaken their north-west rivals to reach the summit for the first time since November with victory in the lunchtime kick-off against Everton.
And while the three points re-established their two-point advantage the less-than-convincing nature of victory against the league's next-bottom side was not quite befitting the occasion of Liverpool's biggest league crowd of 60,725 after the full opening of the Anfield Road stand.
For a time it appeared the hosts, who due to flu in the camp were without goalkeeper Alisson Becker and Joe Gomez, were still suffering a hangover from the defeat at Arsenal last week.
It took the familiar right boot of Trent Alexander-Arnold, setting a new mark of 58 for Premier League assists by a defender, and the equally reliable head of Diogo Jota to get them out of first gear but even then it was far from a return to normality.
The sloppy concession of an equaliser to Dara O'Shea on the stroke of half-time posed further problems as did the withdrawal of Alexander-Arnold - only recently returned from a knee injury - at half-time.
But it was the England international's replacement Harvey Elliott who set up goals for Luis Diaz and Darwin Nunez to ease the pressure.
However, had on-loan Chelsea forward David Fofana been as clinical as he was scoring twice last weekend then not only would Liverpool still be looking up at City but questions would have started to be asked about their ability to match their long-time rivals blow-for-blow.
They do have Mohamed Salah and Dominic Szoboszlai to return from injury in the next couple of weeks but having negotiated January without the pair it was imperative they regained their momentum after their Emirates setback.
For 25 minutes it looked a struggle with Caoimhin Kelleher required to be out quickly to block Zeki Amdouni's shot as early as the 10th minute as Klopp's side struggled to find any rhythm.
Alexander-Arnold and Curtis Jones both fired rising shots over until, just past the half-hour, the breakthrough came when Clarets goalkeeper James Trafford misjudged the flight of a corner and Jota headed in his fifth goal in six games.
But O'Shea produced a better header from 12 yards from Josh Brownhill's corner, outjumping Wataru Endo, now back from the Asian Cup, to power the ball past Kelleher.
Jones moved to right-back to fill in for Alexander-Arnold at the start of the second half but within seven minutes Elliott had made his first significant contribution when his low cross took a deflection off Maxime Esteve and allowing a stooping Diaz to nod in at the near post.
But although playing better they still looked far from secure and Kelleher made a huge save in the 64th minute in a one-on-one against Fofana, with Wilson Odobert blazing over the rebound, before the Burnley forward steered a shot wide of the far post with only the goalkeeper to beat.
Visiting sides rarely get the chance to squander such chances and after Jota had a shot tipped around the post, Jarell Quansah volleyed wide and Virgil van Dijk headed at Trafford it was left to Nunez to apply the finishing touch when he flicked a header inside the far post from Elliott's cross.
The Uruguay international had a chance to make the scoreline more flattering in added time but, typically, shot straight at Trafford.