Firmino got the first, with Mane and Salah adding goals either side of half-time, substitute Daniel Sturridge making it four with 13 minutes left.
Liverpool quick out the blocks
A quick start had seen Liverpool blitz Bundesliga side Hoffenheim in mid-week, and they looked to deploy the same tactic against the Gunners.
Emre Can flashed a header wide from an Alberto Moreno cross, before turning provider himself.
Exchanging a neat one-two with Georginio Wijnaldum, Can burst down the left hand side of the penalty area and produced a fantastic low cross for Mohamed Salah, steaming in at the back post, with Petr Cech getting across goal brilliantly to prevent the Egyptian from opening the deadlock.
What Cech couldn't manage, though, was stopping Firmino from making it one-nil a matter of minutes later.
Involved again, Can laid it off to young Joe Gomez down the right, with the centre-back by trade floating inside to whip in a lovely ball on his weaker left-foot, Firmino making no mistake as he powered a header home from the edge of the six-yard-box.
Reds dominant as they Mane makes it two
It could have been two minutes later thanks to some effective pressing from Jordan Henderson. Winning the ball back, the skipper then benefitted from Firmino's through ball, his resulting dink pulling a little too wide of Cech's goal.
Loris Karius had been a surprise inclusion in the home goal, picked ahead of Simon Mignolet, and he did little to calm the nerves about his selection as a clearance thundered back off Arsenal forward Danny Welbeck.
That was swiftly forgotten, mind, as the Reds kept up their constant waves of attacking football.
Mohamed Salah, seeking his first Anfield league goal, forced Cech into a save, driving inside from the left and crashing a low shot towards the back post.
Counter-attack of sheer beauty
The second-goal did come for Liverpool just five minutes before the break, the man on the opposite flank to Salah scoring it.
Joe Gomez played a part again, launching Liverpool's counter-attack with a superb interception as Arsenal looked dangerous.
Shifting it to Wijnaldum, and then from the Dutchman to Can, Liverpool were mesmeric as they streamed forward at pace. Firmino, adding an assist to his goal, weighted his pass to the rapid Mane perfectly, with the Senegalese winger making no mistake as he dribbled inside from the left and wrapped a delicious finish across goal and into the bottom corner.
Arsenal changes pay little effect
Arsene Wenger looked to change things for the second-half, bringing Francis Coquelin on for Aaron Ramsey at the break. Unfortunately for the French boss, it made little difference.
Having seen fellow forward-liners get on the score-sheet, Salah looked like he fancied some for himself and grew even further into the game with Arsenal still on the back-foot.
Robbing the ball from Monreal, Salah burst through on goal and had a good effort saved by Cech, Jordan Henderson doing well to get to the rebound but ultimately shooting over.
Salah's pressing presented him with another chance some time after, resulting in Liverpool's third goal coming from an Arsenal corner.
Joel Matip's headed clearance fell to the feet of Hector Bellerin, whose touch let him down. Capitalising, Salah pinched the ball and again left the Arsenal defence in his wake once more, bearing down on the 'keeper and finishing well for the third.
Sturridge on to complete rout
Bellerin went from giving a goal away to saving one as the demolition continued, clearing from the line as Mane stung Cech's palms inside the area.
He couldn't do anything about number four though, substitute Daniel Sturridge getting in on the act on a day where everything Liverpool touched turned to gold.
Breaking again, Jürgen Klopp watched in delight from the side-line as Emre Can was once more heavily involved, breaking forward to slide the ball down the left for Salah, his out-swinging cross reaching Sturridge, who broke away from Laurent Koscielny at the back post to nod in.
By that point, Wenger had again turned to his bench as Anfield saw the introduction's of Olivier Giroud and Alexandre Lacazette. However, with Oxlade-Chamberlain and Sanchez coming off, it only opened the gates more for Liverpool to break away.
There wasn't to be a fifth, Liverpool's pace-men going down the gears as the game entered the final few minutes, with the game well won.