The former England captain came on with only a few minutes remaining, but was given his marching orders in stoppage time for a rash challenge, meaning PSG finished with nine men.
The former England captain was brought on for Jeremy Menez with six minutes remaining, but saw red in injury time for an over-the-ball challenge on Youssef Adnane.
Although no contact was made with the Evian forward, Beckham went in well over the ball and stamped down with his studs showing.
PSG had gone ahead thanks to Javier Pastore's goal five minutes after the break, and was already down to 10 men by the time Beckham came on due to Marco Verratti's dismissal for two bookable offenses.
Parisien goalkeeper Salvatore Sirigu was also sent off following the final whistle, and he was joined by Evian's Saber Khelifa.
Carlo Ancelotti's men sit nine points clear at the top of Ligue 1 with four games remaining.