The capital club saw off fellow challengers Marseille 2-0 thanks to Lucas Moura’s deflected first-half goal and Zlatan Ibrahimovic’s late clincher.
Beckham was a 76th-minute replacement for Javier Pastore, and he supplied a fine through ball for Ibrahimovic’s 90th minute goal.
St Etienne kept the pressure on in the battle for Europe as they brushed aside rock-bottom Nancy 3-0.
Brandao’s opener and a brace by Pierre-Emerick Aubameyang sealed a routine victory for St Etienne.
The win puts St Etienne fifth, just two points behind Marseille.
Montpellier moved up to sixth with a 1-0 win away to Evian, with Younes Belhanda scoring 10 minutes from time in a smash-and-grab raid on their relegation-battling hosts.
Sixth-placed Rennes lost ground in the European battle after a 2-2 draw at home to Sochaux.
Lille moved to within a point of Rennes after Yohann Poulard’s own-goal six minutes before half time put them on the road to 3-1 win at Ajaccio. Although Lucas Digne then saw red in the 61st minute, a brace from Dmitri Payet wrapped it up before Chakhir Belghazouani’s late consolation for the hosts.
Struggling Troyes took a point off Bastia in a 0-0 draw while the mid-table clash between Valenciennes and Toulouse also finished goalless.