The Reds hosted the Gunners at Anfield in the weekend’s standout top-flight fixture.
The home crowd were in wonderful voice before kick-off, producing a particularly impressive rendition of You’ll Never Walk Alone.
During a one-sided first half, Joel Matip gave Liverpool the lead with a bullet header in front of the Kop, celebrating his first goal since last September.
It’s two goals already this season for the centre-back, who managed just one in each of his three previous seasons at Anfield.
After a trademark lapse in concentration from David Luiz, fouling Mohamed Salah inside the penalty area, the Egyptian fired home the subsequent spot-kick.
It was a comfortable and composed penalty from the Reds’ No.11, into the top corner.
It was soon 3-0, as Salah embarrassed Luiz before finishing superbly, wheeling away in delight after finding the net.
Lucas Torreira may have scored a late consolation, but Unai Emery knew his side had been comprehensively outplayed as he shook hands with Klopp.
Next up for Liverpool is a trip to Burnley at the same time next Saturday, with victory at Turf Moor making it Liveprool’s longest winning league run (13) in their history.