Strugglers Monaco went 2-0 up despite being one man down early on, but finished the match exhausted as Guingamp forced a shootout to reach the final against either Racing Strasbourg or Girondins de Bordeaux in Lille on March 30.
Monaco's William Vainqueur was sent off after 14 minutes for a dangerous tackle but the visitors stayed focused and went ahead four minutes later when Rony Lopes found the back of the net with an overhead kick.
Monaco, with Jardim on the bench for the first time since he replaced Thierry Henry last week, doubled their tally in the 28th minute as Aleksandr Golovin scored with a powerful shot after being set up by Lopes.
Playing with 10 men eventually wore Monaco down and Guingamp pulled one back 16 seconds into the second half when Alexandre Mendy beat Danijel Subasic with a low shot.
Marcus Thuram levelled in the 55th minute with a 20-metre strike.
Guingamp coach Jocelyn Gourvennec replaced keeper Karl-Johan Johnsson with shootout specialist Marc-Aurele Caillard and the move paid off as he saved two penalties and saw Sofiane Diop's effort crash against the bar.
Monaco, second from bottom in Ligue 1, must now focus on staying in the top flight having shown improvement under the returning Jardim, who was sacked by Monaco last October before returning last week.
(Reporting by Julien Pretot; Editing by Toby Davis)
