Edinson Cavani had levelled matters after Daniel Congre opened the scoring, but the Colombian struck in the second half to put the French champions out of the Coupe de France
Blanc's side had opened their Ligue 1 campaign with a frustrating draw away to the same opponents, but saw any hopes of a quadruple go out the window courtesy of a 2-1 home defeat.
They dominated the early proceedings, as Lucas Digne had a goal disallowed for offside, while Blaise Matuidi also spurned a golden opportunity.
Montpellier took the lead completely against the run of play, as a goalkeeping blunder from Nicolas Douchez saw Daniel Congre head into an open net in the 20th minute.
Digne squared for a Cavani equaliser 10 minutes later, but the match was decided by Montano's bullet header from a corner in the 69th minute.