Edinson Cavani had leveled 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 its Ligue 1 campaign with a frustrating draw away to the same opponents and saw any hopes of a quadruple of titles go out the window courtesy of a 2-1 home defeat.
The Parisiens 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 equalizer 10 minutes later, but the match was decided by Montano's bullet header from a corner in the 69th minute.