PSG almost fell behind in the opening minutes when their defence was caught ball-watching, allowing Quentin Cornette to find space in the danger zone and get a shot away, forcing an early save out of Alphonse Areola.
The visitors took around 20 minutes to find their rhythm and launched their first attack of note when former Manchester United winger Angel Di Maria smashed a volley narrowly wide.
The Ligue 1 table-toppers should have made it two on the half-hour mark when chances fell to Nkunku and Di Maria in rapid succession, but Gurtner reacted quickly to deny the youngster and then the Argentine on the rebound.
The Amiens goalkeeper pulled off another impressive stop moments before half time as Di Maria latched on to a cross in the box and hit a shot towards the top corner, only to be thwarted by the home stopper's acrobatics.
Amiens were quick off the blocks in the second period and they drew themselves level just two minutes into it when Konate took advantage of a defensive lapse and beat Areola with a low shot from close range.
The visitors had the chance to register an immediate response through Giovani Lo Celso, who collected the ball from Cavani and pulled the trigger, blazing his effort wide of the target.
The parity lasted until just after the hour when Nkunku used his skill and pace to carve out space inside the box and curled an unstoppable effort straight into the top corner to make it 2-1.
After edging their noses back in front, PSG remained the dominant side but Amiens nicked a point in the final 10 minutes thanks to an error from Areola.
Konate found space inside the box again and rolled a tame shot towards goal, which the Frenchman dived over and watched it trickle into the net to level the contest for the second time.
With less than 10 minutes remaining, PSG pressed for a winner and nearly found one late on when a volley that Cavani hit into the ground almost bounced into the net, kept out only by a line clearance from Bakaye Dibassy.
Stoppage time was nervy for the home side as two last-ditch chances fell to Di Maria, but the Argentine international could not find a way past Gurtner.
PSG's unbeaten run in domestic matches now stands at 10 games running following the draw, while a point for Amiens leaves them in 12th place in the league table.
AMIENS (4-2-3-1): Gurtner; Cissokho, Adenon, Dibassy, Avelar; Monconduit (Fofana 74'), Zungu; Cornette (Gakpe 66'), Kakuta, Manzala (Bodmer 81'); Konate
PARIS SAINT GERMAIN (4-3-3): Areola; Meunier, Marquinhos, Kimpembe, Kurzawa; Lo Celso, Thiago (Rabiot 78'), Nkunku (Mbappe 84'); Di Maria, Cavani, Pastore