The fourth-round contest took place just two days after a bombshell announcement that rocked English football and that preciously few outside of the club saw coming, with the Anfield crowd showing their admiration and love for their iconic outgoing manager on an emotional afternoon on Merseyside.
Klopp's players did that too in their own way on the pitch, producing a vibrant attacking performance full of goals to advance in the FA Cup and ensure that the German is still fighting for glory on four fronts in what will be his final campaign at the helm.
Liverpool also teed up a Carabao Cup final clash with Chelsea at Wembley next month after getting past Fulham in midweek, while they boast a five-point lead at the Premier League summit ahead of successive games against Chelsea and Liverpool and have also qualified for the Europa League last 16.
The Reds dominated from the outset against a Norwich side managed by Klopp's good friend and former right-hand man David Wagner showing six changes from their midweek Championship defeat by Leeds after a particularly stirring pre-match rendition of iconic club anthem 'You'll Never Walk Alone', taking a deserved early lead when teenage midfielder James McConnell's excellent cross was steered in by Curtis Jones at the back post.
It already looked likely to be a long afternoon for the visitors, play-off chasers in the second tier, who struck back quickly against the run of play when a corner bounced in off defender Ben Gibson.
But Darwin Nunez rapidly restored the Liverpool lead, taking a touch before lashing instinctively into the bottom corner after sloppy Norwich were once again dispossessed inside their own half and another young hopeful, Conor Bradley, played a delightful one-two with Diogo Jota before teeing up the Uruguayan.
They could and should have been much further ahead at the break as the chances continued to pile up, but it mattered little as the opportunistic and lethal Jota rifled in his third goal in the space of a week on the half-volley early in the second half after Gibson could not head clear a long ball forward from Jones.
Captain Virgil van Dijk powered home a header from a corner delivered by fellow substitute Dominik Szoboszlai just beyond the hour mark, with overmatched Norwich then finally gaining some attacking impetus with a couple of changes as Christian Fassnacht saw a goal ruled out for offside before Borja Sainz rifled a beauty beyond Alisson to make it 4-2.
However, they could not find a third goal to truly make things interesting as Liverpool instead poured forward in search of a fifth of their own to put the game to bed, getting it with a last-gasp Ryan Gravenberch header from close range after Luis Diaz's cross had been volleyed into the floor by the impressive right-back Bradley.
Liverpool were able to introduce Szoboszlai and Trent Alexander-Arnold off the bench after injury, while Andy Robertson came on for his first appearance since early October following shoulder surgery - all key boosts for Klopp with that huge showdown against title rivals Arsenal looming.
The only negative for Klopp was a knock that curtailed an impressive showing from young McConnell, with more Championship opposition to come in the last 16 in the shape of either Watford or Southampton, who will require a replay after Stuart Armstrong's last-gasp equaliser for the Saints to cancel out an early opener from Matheus Martins at Vicarage Road on Sunday.
The fifth-round draw was delayed and took place at half-time of Liverpool vs Norwich following serious crowd trouble in the early clash between West Brom and Wolves that saw the Black Country Derby at The Hawthorns suspended for 34 minutes before eventually being restarted and completed.