Having to improvise a new look did not stop Liverpool from parading their customary attacking brio on the Sussex coast and where Brighton have never had it so bad – at least at the Amex Stadium. They moved in six years ago and their current manager, Chris Hughton, declared Liverpool to be the best team they have faced this season – which is high praise considering that the only other visitors to win here were Manchester City.

The endorsement seemed justified because Liverpool were scintillating going forward, with Mohamed Salah, Roberto Firmino and Philippe Coutinho exceptional as Jürgen Klopp’s team brought their goal tally to 15 from their last four away matches.

Yet Klopp was not quite as impressed as Hughton. “Results-wise it looks like we’re flying but we’re not,” said the German, who bemoaned a 10-minute spell in the second half during which his team conceded a goal and risked losing control of the match.

The frequency of such periods is, perhaps, the chief difference between them and Manchester City. This time, at least, there were mitigating factors.

Joël Matip’s injury and Ragnar Klavan’s illness forced Klopp into a newlook formation in which Emre Can and Georgino Wijnaldum flanked Dejan Lovren in a three-man defence.

With Trent Alexander-Arnold and Andy Robertson playing as wing-backs, Liverpool’s backline had an avant-garde look. But the shape was mostly anecdotal as Liverpool were fluid and devastating when in possession, which was most of the time.

Brighton found it quite the brain-teaser. They were stumped by the visitors’ speed and movement, especially in the first half.

Salah fired off the first shot after less than 30 seconds, signalling the fusillade that was to come.

Salah and Firmino both went close again before Brighton exposed any uncertainty in Liverpool’s rejigged defence. That was in the 17th minute, but Glenn Murray miscued after Can and Lovren failed to cut out a cross by Izzy Brown. It was the last glimpse that the home side would get of Liverpool’s net before the match was put beyond them by two goals in 79 seconds.

On the half-hour, Can sent a powerful header into the net from a corner by Coutinho. Then Liverpool doubled their lead with a breakneck counterattack, Salah leading the charge before flipping the ball wide to Coutinho, whose low pass from the left was turned in by Firmino.

Emre Can heads Liverpool in front with half an hour played. Photograph: Mike Hewitt/Getty Images

With Sadio Mané resting on the bench in advance of Wednesday’s decisive Champions League tie at home to Spartak Moscow, Coutinho was Liverpool’s ringmaster, tormenting Brighton with the sort of flourishes that prompted Barcelona try to sign him in the summer. Yet Liverpool’s habit of frittering away leads means opponents can always hope for a comeback.

Brighton evidently still believed it was possible when they emerged after half-time, and their faith would have been rewarded within two minutes if not for a brilliant save by Simon Mignolet. Brown created the chance by sneaking into the space behind Alexander-Arnold, but Mignolet saved Murray’s close-range volley with his feet.

Before Brighton knew it, they were three goals down, Liverpool racing up the other end of the pitch for Firmino to finish emphatically after being served by Salah.

Three minutes later, however, Brighton narrowed the gap. This time it was Liverpool who did not grasp what was happening. The referee, Graham Scott, awarded the home team a penalty for an offence he saw as the ball was floated in from a corner. Liverpool’s defenders looked bemused, but Murray asked no questions and converted from the penalty spot.

Liverpool did not disintegrate. They blew Brighton to pieces. Coutinho crowned his regal performance with a goal of craft and slyness.

Anticipating that Brighton’s players would jump, the Brazilian drilled a 20-yard free-kick under the wall and into the net.

“Credit to the analysts,” said Klopp, explaining that Liverpool’s backroom staff had tipped off Coutinho about the behaviour of Brighton’s wall. “But you still have to have the skill to do it,” added the manager in praise of the Brazilian, who scored a similar goal against West Ham United last year.

Hughton described the dilemma facing opposing teams when Coutinho is standing over a free-kick. “If you don’t jump, he whips it into the top corner,” he said. “You have to give the credit to the player.”

Lewis Dunk would have liked Coutinho to be credited with Liverpool’s fifth goal, too, otherwise the record must identify the Brighton defender as the culprit, as he inadvertently diverted the Brazilian midfielder’s shot into his own goal in the 89th minute.