Giroud heads Montpellier into League Cup final
The hosts were helped by the 88th-minute dismissal of PSG midfielder Clement Chantome who was shown a second yellow card after a late tackle on Gary Bocaly and left his team-mates to face the 30 minutes of extra-time with 10 men on Tuesday.
Giroud clinched the semi-final win when he headed home a Geoffrey Dernis cross. The woodwork saved Montpellier in the dying seconds when Jean-Eudes Maurice's shot was deflected on to the post.
Minutes earlier, Guillaume Hoarau had wasted PSG's best chance when he narrowly missed the target after being perfectly set up by Maurice's fine cross from the right.
On Wednesday, holders Olympique Marseille travel to AJ Auxerre in the other semi-final.
The final will be played at the Stade de France on April 23.