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Les Parisiens doubled their advantage in the 25th minute when a well-placed cross from Serge Aurier was met by Lavezzi, who duly turned his effort beyond Ligali's reach.
La Paillade almost found themselves three down inside the opening 31 minutes when Cavani was afforded space in the area to shoot, but the young Montpellier keeper was able to tip the Uruguayan's shot around the left-hand post.
Instead, the hosts managed to pull a goal back in comical fashion as a shot from Anthony Mounier, which was almost certainly intended to be a cross, managed to lob Salvatore Sirigu and dip under the crossbar.
Montpellier were not far away from equalising early in the second half as substitute Bryan Dabo drilled a shot wide of the target.
PSG came close to finding a third goal late on as Javier Pastore struck the woodwork in stoppage time, but they were able to hold on for victory that confirms their title triumph and takes them two-thirds of the way towards a first domestic treble in French history.