The hosts rained 14 shots in at Benoit Costil's goal, but the visiting goalkeeper produced a fine display to snaffle a point for his side.
Rennes moved up to fifth with the point, their third goalless draw of the season, while Montpellier also climbed the table to 13th.
But the 2012 champions should have had more with Anthony Mounier guilty of blasting over in the first half as Montpellier quickly asserted their dominance.
Remy Cabella was too denied by Costil before firing into the side netting on the stroke of half-time.
The second half followed a similar pattern as the former Sedan keeper produced arguably his best saved of the night to deny Colombian forward Victor Montano.
Montpellier just could not find the required magic to beat the in-form 26-year-old and will hope for better when they travel to Ajaccio on Sunday, while Rennes host Nantes in a Breton derby.
