Lucas opened the scoring with just 19 minutes to go but the forward earned the visitors a point with his last-gasp equaliser
The defending champions lived dangerously for much of the encounter, with Yannick Ferreira Carrasco and Layvin Kurzawa going close for the visitors either side of the break.
Lucas Moura exposed a gaping hole in the Monaco defence to give PSG the lead in the 71st minute, and the hosts looked set to claim all three points at the Parc des Princes as the game entered the closing stages.
However, Martial stepped off the bench to lift the ball over goalkeeper Salvatore Sirigu in second-half stoppage time and earn his side a share of the spoils.
The men from the French capital 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 this - the fifth consecutive Ligue 1 stalemate between the sides - as a positive result.
PSG made just one change to the side that beat Barcelona 3-2 in the Champions League on Tuesday, with Zoumana Camara coming in for the injured Marquinhos, while Ferreira Carrasco took the place of Dimitar Berbatov – sidelined by an ankle problem – in the Monaco XI.
After legendary sprinter Carl Lewis had taken part in a ceremonial kick-off, the match appropriately began at a frantic pace, with PSG's Marco Verratti the first to get a sight of goal.
However, the Italian lifted his seventh-minute effort over the crossbar after being teed up by Lucas Moura.
Lucas Ocampos squandered a similar opportunity when he fired over at the other end eight minutes later, before PSG had a penalty appeal turned down.
Edinson Cavani hit the floor under the challenge of Andrea Raggi in the box after 22 minutes, but referee Benoit Bastien was right to wave away the home side's protests.
Despite both sides maintaining a high tempo, a lack of quality in the final third meant that their respective goalkeepers enjoyed a relatively quiet first half.
But Sirigu had to be alert a minute before the break – getting the slightest of touches to a fierce Ferreira Carrasco strike to force the ball onto the crossbar.
The first 10 minutes of the second period passed without incident, before substitute Jean-Christophe Bahebeck forced Monaco goalkeeper Danijel Subasic into a one-handed save from a tight angle.
Monaco then had arguably their best chance to break the deadlock, when Sirigu palmed the ball into the path of Kurzawa, whose subsequent half-volley was desperately cleared off the line by Gregory van der Wiel.
PSG appeared to have snatched victory in the 71st minute, when Lucas Moura was allowed to stroll into the area unmarked to convert a simple tap-in, after Bahebeck had squared the ball from the right.
But Monaco had the final say, with Martial - on as a 76th-minute replacement for Ocampos - benefiting from PSG's failure to clear their lines and lifting the ball over Sirigu from close-range.