Philippe Coutinho shone as Liverpool put in a five-star show on the south coast to see off Brighton at the Amex Stadium.
The Brazilian was at his very best as Jurgen Klopp's Reds proved too sharp for Chris Hughton's lethargic Seagulls.
Klopp continued his rotation policy with six changes and a switch to a back three, with Dutch midfielder Gini Wijnaldum out of position as one of the three centre-halves.
And it was one of his defensive partners, Emre Can, who handed the Reds the lead with a towering first-half header.
Within 80 seconds that lead was doubled, a sweeping counter attack seeing Mohamed Salah find Coutinho, who put it on a plate for compatriot Roberto Firmino.
Salah, the Premier League's top scorer, failed to add to his tally but again helped assist Firmino, moments after Murray had been denied by a brilliant Mignolet save.
Murray got his name on the score sheet shortly after, confidently scoring from the penalty spot after a push from Jordan Henderson on Shane Duffy.
That could have flustered the visiting side, but they instead retained their composure, before Coutinho put the game beyond doubt and added some shine to the score-line late on.
First, he wrapped up the result with a clever freekick, firing under the wall as it jumped.
And two minutes later, his shot on goal was headed into his own net by the hapless Lewis Dunk.
Here are five talking points from the Amex...
1. Klopp's changes do the business
Klopp has made no bones about his rotation policy lately, looking to keep all his players fresh for the busy winter period.
On the south coast he once more made six changes, including Sadio Mane dropping to the bench and the return of both Coutinho and Salah.
And seemingly his quest to keep his players fresh for the challenges to come is working, with the Reds looking for more energetic than their hosts, who looked rather leaden-footed whenever Liverpool stepped it up a gear or two.
Klopp's changes didn't just extend to the personnel however. With Joel Matip absent, Klopp named only one recognised centre-half (Dejan Lovren) in his lineup and instead switched to a 3-4-2-1 formation, with Emre Can and Gini Wijnaldum playing to the right and left of Lovren respectively.
Wijnaldum initially looked uncomfortable but grew into the role, while Can - no stranger to playing in the backline - made key contributions at both ends.
2. Coutinho thriving once more
Perhaps two months or so ago it was easy to say that if Barcelona offered in excess of £100million for Philippe Coutinho, then Liverpool should seriously consider taking it.
The Brazilian’s adaptation to a deeper role in midfield hadn’t fully gone to plan and the Reds were in the midst of a little dip in form.
Nonetheless, Coutinho’s numbers throughout have continued to be excellent, even at times when perhaps his performances weren't up to his usual high standards; after today, he has played a direct hand in 13 goals in his last 10 Premier League games (seven goals, six assists).
However, Coutinho was very much back at his effervescent best on the south coast, playing as part of the front three. The little shimmies and clever touches were all there, and Brighton simply had no answer, unable to contain his stealthy movement and incisive passing.
His freekick, for Liverpool's fourth, was just wonderful; faced with a tall Brighton defence, he had the presence of mind to go low, rolling it under a jumping wall and into the bottom corner.
Liverpool will hope his head isn't turned once more in January.
3. Murray misses prove costly
Eventually Glenn Murray got his goal, the Brighton striker converting from the penalty spot in the 51st minute.
By then however, the veteran striker had missed two standout opportunities and his side were 3-0 down.
As the game was settling down early doors it was Murray who had the opening chance of the match; Gaeton Bong's cross found the Seagull striker, who was on the half turn as Gini Wijnaldum tried to put him off. Murray elected to swivel and shoot from six yards instead of teeing up Pascal Gross; the wayward effort flew well wide, leaving the German unhappy not to have been given the chance.
Murray would then be denied by a brilliant Mignolet save three minutes into the second half (at 2-0), having got in front of his marker. Within 60 seconds, it was 3-0.
The 34-year-old is Brighton's top scorer with five goals now this season, and Chris Hughton will be pleased that the veteran hitman is getting chances at the top level. However, there can be no doubt that he needs to be more ruthless.
4. Salah's evolution continues
The Premier League's top scorer didn't help himself to his 13th goal of the season, but he is continuing to mature into an outstanding all-round attacker.
During his times at Basel and Chelsea it was easy to deride him as just another speed merchant, always looking to spin off the back of opposing defences and get in behind.
But the Egyptian has added to his game, become more tactically intelligent during his Italian sojourn, and is now adding more attacking weapons to his armoury.
That maturation continues with Salah increasingly looking more and more at home playing through central areas, making himself not only an increasing threat in transition, but also in tightly-packed central areas.
It was Salah in transition who took the game away from the Seagulls, countering and playing the right pass for the second, before doing similar for the third.
His evolution is proving a thrilling watch and that £37million looks a bargain already.
5. All about bouncing back for Brighton
It isn't home defeats to the likes of Liverpool that will define Brighton's season, rather how they react to them.
Next weekend the Seagulls head to Huddersfield, a side tumbling down the table after an initial bright start.
Hughton needs to pick up his players after this result, and reinvigorate a side that, for spells here, looked lethargic, one-paced and largely frustrated - all despite actually creating chances when they did offer some fleeting attacking threat.
Next weekend's game gives them a chance to be far more pro-active and to take the game to their opponents - something the likes of Anthony Knockaert, Davy Propper and Izzy Brown will likely prefer, having spent much of this game chasing between Liverpool players.