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Pierre Berard added a third try after the break to give the visitors a comfortable lead, which enabled them to dominate the game.
The French side were coasting for much of the second half as Sale rarely threatened the try line, struggling with the visitors' pace.
Montpellier were awarded a penalty try late in the game to seal the victory.
The win for Montpellier keeps the pressure on pool leaders Toulon, while Sale could drop to the bottom of the pool if Cardiff Blues win tomorrow.