PSG's task was made hard in the first half when Zlatan Ibrahimovic was given his marching orders for tangling with Brazilian playmaker Oscar.
But the French giants took the tie to extra time and skipper Thiago Silva scored a late header to break Blues hearts.
The captain looked to have cost his team when he handled and allowed Eden Hazard to restore Chelsea’s lead at the start of the additional 30 minutes.
Hazard had calmly slotted home from 12 yards after David Luiz had cancelled out Gary Cahill’s opener to force the game to go the distance.
Chelsea must now focus their attentions on securing the Premier League to add to their Captial One Cup triumph.