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Plisson kicked three in the first half and four more in an error-strewn second period in Paris to hand Stade a confidence-boosting win in what has so far been a troubled season.
Montpellier scored the only two tries of the game, Australian Joe Tomane and Fijian Timoci Nagusa crossing for Jake White's team.
But it was all too little too late as Plisson kept Stade ticking over and up to 10th in the table, with Montpellier in fourth.
On Saturday, Morgan Parra hit an injury-time penalty to help consolidate Clermont's lead atop the table with a 16-13 victory over Lyon.
Bordeaux-Begles surged into second with a convincing 26-0 win over La Rochelle, now third on points difference.