An epic second half initially saw a rampant Liverpool double their advantage shortly after the restart, Salah's shot deflecting in after Firmino led a superb counter-attack.
Arsenal scored three goals in quick succession, inside five minutes to be exact, helped by some lackadaisical Liverpool defending and calamitous goalkeeping from Simon Mignolet.
"A point at Arsenal is a good result for most teams in the world but it feels not too good at the moment".
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Coutinho, who is best known for scoring spectacular goals with his feet, showed great awareness to steer his header into the Arsenal net and take his tally to 11 in all competitions this term.
Liverpool have now drawn three of their last four Premier League matches.
Sky Sports pundit Charlie Nicholas had some surprise answers when asked to pick his Arsenal and Liverpool combined XI.
However, only a minute later Alexis Sanchez gave the Gunners an immediate lifeline by heading home a lovely whipped cross from Hector Bellerin.
Sanchez nearly beat Mignolet at his near post before the late introduction of Alex Oxlade-Chamberlain off the bench created the enticing possibility of the former Gunners midfielder punishing his former employers.