Laurent Blanc's men were under pressure for much of the contest and could count themselves fortunate to be on level terms approaching the closing stages after Yannick Ferreira Carrasco and Layvin Kurzawa had gone close for the visitors either side of the break.
But Lucas Moura broke the deadlock for the home side at the Parc des Princes in the 71st minute when he exposed a gaping hole in the Monaco defence to tap home from close range.
That seemed set to give PSG the victory, as they seek to bounce back from a below-par start to the campaign by their own high standards.
However, Monaco had the final say, with Martial - on as a 76th-minute replacement for Lucas Ocampos - benefiting from PSG's failure to clear their lines and lifting the ball over goalkeeper Salvatore Sirigu in stoppage time.
PSG remain unbeaten in the league, but they have now drawn six of their nine matches so far this season, and sit seven points adrift of early leaders Marseille.
Monaco, meanwhile, have already lost as many matches as they did last season, and will likely view Sunday's result - the fifth consecutive Ligue 1 stalemate between the sides - as a positive outcome.
Lille also lost ground on Marseille as they were comfortably beaten 3-0 by Lyon, with Alexandre Lacazette netting his first career hat-trick.
The 23-year-old was overlooked for Didier Deschamps' latest France squad, but he set the ball rolling with a cool finish in the 39th minute, before doubling his tally by heading home from a Yoann Gourcuff free-kick on the stroke of half-time.
Lacazette's treble was complete in the 84th minute when he beat Lille captain Marko Basa before sending the ball beyond goalkeeper Vincent Enyeama.
Like PSG, Lille are now seven points adrift of Marseille, while Lyon - unbeaten in five league matches - are a point further back.
Guingamp's dismal start to the season continued as they were beaten 1-0 at home by Nantes.
Georges-Kevin N'Koudou found the top right-hand corner of the net from outside the box in the 33rd minute to send Nantes level on points with Lille and PSG, while Guingamp remain rooted to the bottom having lost their last four matches in the league.
In the day's other fixture, Toulouse triumphed 1-0 over Saint-Etienne thanks to Wissam Ben Yedder's 22nd-minute strike.
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