The 2008 winners ended the game with 10 men after loan signing Scott Allan was sent off after 75 minutes, which cued a touchline melee that saw Pompey's first team coach Ashley Westwood sent to the stands.
Notts County should have led after 18 minutes when Jamal Campbell-Rice danced his way down the right. He squared it to Arquin, who miscued his shot on to the crossbar.
But the Magpies stole ahead in first-half stoppage time when Zoko nodded home Alan Judge's looping cross from the right.
County doubled their lead after 56 minutes when Campbell-Rice hung up a beautiful cross from the left, which Arquin netted with a textbook header.
Pompey's plight worsened after 75 minutes, when Allan was given a straight red card for kicking Campbell-Rice - just three minutes after being cautioned for felling the County winger.