Ben Arfa, who has only started five Ligue 1 games this season after joining from Nice, struck each side of the interval as the defending champions joined En Avant Guingamp, Angers and Monaco in the last four.
PSG were without striker Edinson Cavani, winger Angel Di Maria, captain Thiago Silva and influential midfielder Marco Verratti, but Ben Arfa inspired the team to a routine win at Caen's Michel d'Ornano stadium.
He put his side ahead as he fired a splendid strike from the edge of the box into the far top corner after his attempt took a slight deflection off Jonathan Clauss's head in the 35th minute.
Ben Arfa, who last month in a video on Instagram asked coach Unai Emery to give him a chance, doubled the tally eight minutes into the second half by tapping in a pass by Lucas.
Brazilian forward Lucas then found the back of the net, firing home after chesting the ball down from Blaise Matuidi's cross on 56 minutes.
Read the full article on eurosport.co.uk: Ben Arfa shines as PSG see off Avranches to reach Cup semis