The timely victory left big-spending PSG three points clear at the top from Lyon, who had beaten Lorient earlier Sunday. Defeat left Marseille eight points adrift.
Beckham, who has played for Manchester United, Real Madrid, AC Milan and LA Galaxy during his glittering career, has signed contract with the Parisian giants until the end of the season.
He has donated his reported 800,000-euro ($1 million) monthly salary to a local children's charity.
Meanwhile, AC Milan striker Mario Balotelli had a less fruitful evening in his first Milan derby match for three years.
Balotelli, signed in the transfer window from Manchester City, missed a string of chances as his side were held 1-1 by his former side Inter, damaging their Serie A title hopes.
Milan, boosted by their 2-0 midweek win over Barcelona in the Champions League, took a 21st minute lead through striker Stephan El Shaarawy.
Balotelli had three clear chances to add to their lead in the San Siro before Inter midfielder Ezequiel Schelotto leveled in the 71st minute.