The 'Red Devils' paid in added time for not having closed the game earlier and are on the brink of entering the 'Champions' zone with three matchdays to go.
United started the match poorly due to an error by Paul Pogba, who was dispossessed by Danny Ings, and the play ended with a shot from Stuart Armstrong that opened the scoring.
The match could have become complicated for United, but they responded to the pressure very quickly.
First, Martial passed the ball from the ground to Marcus Rashford, who equalized with his left foot, and a few minutes later Martial himself penetrated the area, moved towards the inside, and scored a powerful shot that meant 2-1.
United could have scored more goals, especially through Rashford, who missed some very clear chances, but they relaxed a lot in the second half and let themselves go against a Southampton side that has nothing at stake and barely threatened David de Gea's goal until stoppage time arrived.
In an isolated corner, a Southampton player flicked the ball on at the near post and Michael Obafemi, at the far post, pushed it in and sealed the final 2-2.
This draw hinders United's Champions League aspirations, as they remain fifth with 59 points, the same as Leicester City and one less than Chelsea with three matchdays to go.
Ole Gunnar Solkjaer's team will play against Crystal Palace, West Ham United, and Leicester City to end the championship.