Thomas Tuchel's side found themselves 3-0 down in the first half following goals from Serhou Guirassy, Gael Kakuta and Fousseni Diabaté. Ander Herrera volleyed in from a corner to give the visitors hope at the end of the opening period before they continued their comeback after the break.
Teenager Tanguy Kouassi's headed double saw PSG draw level at 3-3 in the 65th minute before Mauro Icardi gave them an incredible unlikely lead.
However, they weren't able to hold on to the victory as Guirassy slotted past Keylor Navas to equalise in stoppage time.
It's not ideal preparation for PSG as they gear up for the first leg of their Champions League last-16 tie against Borussia Dortmund on Tuesday, although Kylian Mbappé was rested with that in mind.
Amiens, meanwhile, will see the draw as a vital point in their bid for survival, despite taking a three-goal lead.