Forward Takumi Minamino also netted, his just 48 seconds after coming off the bench late in the game to help rout Arsenal.
Manager Jurgen Klopp's side moved up to second place in the Premier League and redeemed their four-point gap behind leaders Chelsea, who briefly sat six points clear at the top with a resounding win over Leicester City earlier on Saturday.
Both managers -- Liverpool's Klopp and Arsenal's Mikel Arteta -- received yellow cards and had to be separated in a heated exchange following a contested header between Mane and Arsenal defender Takehiro Tomiyasu.
The incident sparked an increased intensity in the game, soon resulting in Liverpool taking the lead through Mane, who headed home a deep cross from defender Trent Alexander-Arnold.
Jota extended the hosts' lead shortly after the restart as he showed impressive footwork to wrongfoot opposing defender Ben White and goalkeeper Aaron Ramsdale before stroking the ball into an empty net.
Salah, who had come close on numerous occasions, added one of his own on 73 minutes, tapping home from a Mane cross.
Minamino removed all hope for Arsenal just minutes later as he scored a similarly easy finish, this time following a drilled cross from Alexander-Arnold.