Former England captain Beckham, who joined PSG on a five-month deal last month, helped to lay-on Zlatan Ibrahimovic's injury-time clincher as Carlo Ancelotti's men claimed a 2-0 triumph at the Parc des Princes.
Brazil international Lucas Moura, another January arrival, had put PSG ahead in the Ligue 1 Classique with a deflected goal in the 11th minute.
The result sees PSG restore their three-point lead at the top of the standings over second-placed Lyon, who had beaten Lorient earlier in the day, while the big-spending capital club are now eight points clear of Marseille in third.
Lyon came from behind against Lorient to win 3-1 and register their first home victory of 2013.
The visitors took the lead at the Stade Gerland in the 11th minute through Jeremie Aliadiere's header before Lisandro Lopez drew things level in the 24th.
Rachid Ghezzal then put OL in front in the 50th minute and Arnold Mvuemba added their third in stoppage time to secure the victory.
In Sunday's other Ligue 1 game Bordeaux suffered a disappointing 2-0 defeat at home to lowly Brest.
A Benoit Tremoulinas own goal and a late Ahmed Kantari penalty confirmed a third consecutive Ligue 1 defeat for Les Girondins and left a dent in their hopes of getting a European spot.