The Uruguayan forward scored the first goal at the Nouveau Stade Bordeaux inside nine minutes, latching onto Jaroslav Plasil's through ball before firing his shot into the bottom corner of Jonathan Ligali's net.
Moments later, Rolan was denied a second by a Ligali save before the young goalkeeper twice kept out Wahbi Khazri.
Rolan finally doubled Les Girondins' lead before the interval with a close-range header, seconds after Clement Chantome's shot was saved.
Montpellier improved after the break, with Lucas Barrios twice going close to pulling a goal back for the visitors.
Despite late efforts from Berigaud and Souleymane Camara, Bordeaux were able to hold on for a maiden victory at the Nouveux Stade.