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The Cottagers looked like being the first side since Real Madrid in February to win at Anfield and the first in the Premier League since Leeds in October 2022 after substitute Bobby De Cordova-Reid’s 80th-minute goal.

However, Japan international Wataru Endo, who had spoken on the eve of the game about how difficult he had found the top flight since his arrival in the summer, sparked the comeback when he stroked home the equaliser seven minutes later.

When Alexander-Arnold struck – his brilliant free-kick for the opener went in off goalkeeper Bernd Leno for an own goal – barely a minute later, Liverpool’s 100 per cent home record was extended to 11 matches to move back to within two points of leader Arsenal.

While thrilling, it was an unnecessary end to a game which the hosts should have controlled much better, especially after the quality of the early goals they scored.

Fulham was operating with a compromised goalkeeper after Leno played almost 100 minutes with a bandaged head having being injured in an eighth-minute incident which saw Mohamed Salah’s goal ruled out for offside after spilling Dominik Szoboszlai’s shot.

But while Liverpool had plenty of attempts on goal, Leno was not properly threatened until it became last-chance saloon territory.

The problem was at the other end where they allowed a team averaging just one Premier League goal a game all season to score three times away for the first time since April, also on Merseyside at Everton.

Either of Alexander-Arnold’s or Mac Allister’s strikes were worthy match winners and the fact they were not will have been of considerable frustration to both players and Klopp.

A trip on Szoboszlai 25 yards out was all the invitation Alexander-Arnold needed as he dispatched a 25-yard free-kick – Liverpool’s 50th of the season – via the underside of the crossbar and Leno.

It had all appeared so easy to that point and part of the problem was a team showing six changes from the midweek win over LASK struggled to get out of second gear.

Worryingly for Klopp, at the start of December it seemed his side lacked the energy needed to properly dominate opponents but even Fulham’s unexpected equaliser four minutes later failed to provide the wake-up call.

The right side was exposed with Alexander-Arnold central covering for Virgil Van Dijk, who was returning from a run upfield, and former Red Harry Wilson squeezed a near-post shot under Caoimhin Kelleher from Antonee Robinson’s cross from the Cottagers’ first attempt on goal.

Retaking the lead in brilliant fashion was only a small part of what was required from the home side.

Luis Diaz’s mazy run caused issues and Kenny Tete’s poor clearance was compounded by Raul Jimenez’s poor header back into the danger area and Mac Allister’s path.

The Argentina international allowed the ball to bounce across his body before unleashing a rising drive which found the same top corner Alexander-Arnold had: his first Liverpool goal and a worthy 500th at Anfield in Klopp’s 219th game at the ground.

Jimenez and Tete made amends with the former flicking on a near-post corner for the latter to nod past Kelleher, making his first Premier League start of the season for the injured Alisson and although he was flagged offside, VAR overruled.

The assistant’s flag did come to Liverpool’s rescue, however, deep into added time when Kelleher kept alive Joao Palhinha’s header and an offside Tim Ream tapped in.

Leno’s legs denied Salah just before interval and although Klopp’s side increased the tempo after the break, the same problems remained with Darwin Nunez’s shot deflected behind and Szoboszlai firing wide from the subsequent corner.

Nunez had yet another game where his contribution was minimal and he smashed an angled drive against the crossbar and also bundled the ball wide after twice being set up by Salah.

Then came the sucker punch as substitute De Cordova-Reid out-jumped Kostas Tsimikas at the far post.

Endo had a header saved and Salah fired over the rebound before the Japan international stroked home the equaliser, setting up Alexander-Arnold to deliver the killer blow.