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The visitors took the lead after just three minutes when Christophe Mandanne rose highest to head home Thibault Giresse's corner.
Concarneau, who ply their trade in the Championnat de France amateur Group D, then stunned their opponents when they equalised in the 21st minute, Christophe Gourmelon toe-poking the ball over goalkeeper Mamadou Samassa.
The holders finished the opening half strongly but Ivan Seznec came flying out of his area to clear at the feet of Mandanne, before Jeremy Pied shot over as Concarneau hung on until the interval on level terms.
The hosts continued to hold on after the restart, and with the clock ticking down, it seemed like they were going to take the match to extra time.
However, Guingamp had the final say, breaking their opponents' hearts when Claudio Beauvue blasted his free kick high into the corner of the net with just a minute left of the game.
Jocelyn Gourvennec's side join Paris Saint-Germain, Saint-Etienne and Auxerre in Sunday's semi-final draw.