The unbeaten Reds took full advantage of Tottenham's surprise defeat to Wolves earlier on Saturday to move further ahead at the summit, with defending champions Man City now 10 points behind.
It looked like Jurgen Klopp's side might be in for a tough examination of their title credentials when Ainsley Maitland-Niles put Arsenal ahead after 11 minutes.
However, the defensively frail Gunners capitulated during the first half, with Firmino grabbing a brace and Sadio Mane and Mohamed Salah also getting on the scoresheet before half-time.
Firmino then completed his first hat-trick for Liverpool after the interval to send Arsenal boss Unai Emery back to north London with plenty to ponder.
It had all started so well for Arsenal, who made the home side pay for failing to clear their lines in the 11th minute, Alex Iwobi and Aaron Ramsey working the one-two before Iwobi put in a perfect cross for Maitland-Niles to slide home.
But the lead lasted just three minutes after a calamity at the back from Arsenal as they failed to clear their lines, gifting Firmino a late Christmas present as he tapped into an unguarded net on 14 minutes.
Two minutes later and the Premier League leaders were ahead, Firmino dancing past some poorly-timed Arsenal challenges before beating Bernd Leno from the edge of the box.
Mane added the third in the 32nd minute after a long ball from Andy Robertson found Salah unmarked at the far post and he put it on a plate for Mane to tap in.
Liverpool wrapped up the points on the stroke of half-time when Salah was upended in the penalty area via a clumsy challenge from Sokratis. The Egyptian dusted himself off to net his 12th league goal of the season.
There was no let-up from Liverpool after the break, Fabinho being denied thanks to a smart save from Leno at his near post.
A fifth was inevitable for Jurgen Klopp's side and it arrived in the 65th minute when Sead Kolasinac was adjudged to have pushed over Dejan Lovren inside the box. Firmino dispatched the spot-kick to complete his hat-trick with his eighth goal against Arsenal in Liverpool colours.
As further chances to register their biggest ever win over Arsenal came and went for Liverpool, the Gunners were left feeling aggrieved they didn't get a penalty when Alexandre Lacazette was brought down inside the box, referee Michael Oliver waving away the protests.
Liverpool are now eight unbeaten against Arsenal and enter Thursday's huge clash with Manchester City full of confidence after a 10th straight league win.