The cup holders are level rivals Marseille on 10 triumphs and they overcame lowly opposition to put themselves in the last four of this season's competition.
Avranches are struggling in the Championnat National and gave a good account of themselves against a team whose annual budget dwarfs their own, but the hosts were undone by a brace of goals from Hatem Ben Arfa and further strikes by Lucas Moura and Javier Pastore.
Ben Arfa scored a deflected free-kick in the first half and netted again eight minutes into the second, before Lucas added a third and Pastore struck late to make the scoreline somewhat cruel on brave Avranches.
Having lifted the Coupe de la Ligue just four days earlier, PSG coach Unai Emery rested the likes of Marco Verratti, Edinson Cavani and Kevin Trapp, but still saw his side cruise to victory, and he will hope that bodes well for Saturday's Ligue 1 clash against Guingamp.
The two sides looked surprisingly well matched as the game began and Pastore played in the unmarked Christopher Nkunku, but his shot flew straight into the arms of Anthony Beuve, before Jamal Thiare countered for Avranches and crossed for Jessy Benet to volley a shot over the crossbar.
It was a very respectable start from the home side, whose commitment helped to bridge the clear gap in quality, and winger Charles Boateng threatened when he broke clear, but his shot lacked the power or the accuracy to beat Alphonse Areola.
Beuve only just kept out a Pastore shot after Ben Arfa breezed through midfield and there was a sense that Avranches would struggle to keep PSG out if they gave away further chances.
After 35 minutes, Lucas won a free-kick on his way towards the penalty area and took it short to Ben Arfa, whose shot took a deflection on its way past Beuve into the far corner of the net.
Christopher Mayulu came close to levelling for the minnows five minutes before the break, only to see his low drive parried away by Areola.
Avranches started the second half as brightly as they had the first and Benet dragged a shot wide of goal, but PSG then ruthlessly tripled their lead inside three minutes.
Lucas' run caught the home defence napping and the Brazilian squared to Ben Arfa who applied a simple finish into the empty net after 53 minutes, and just three minutes later Lucas chested down a deflected Pastore cross and slid the ball under Beuve and into the net to make it 3-0.
Knowing they were beaten, Avranches relaxed and played some good attacking football, but Thiare's fierce shot from the edge of the box dipped over the crossbar before Ben Arfa turned provider in the 82nd minute, playing a sweetly timed throughball for Pastore to chip over Beuve and into the net, ending the Normandy club's dreams of a giant killing.