Ben Arfa double puts PSG in French Cup semis
It keeps alive PSG's hopes of a third consecutive clean sweep of domestic honours and they join Ligue 1 title rivals Monaco and Guingamp and Angers in the last four.
But the Parisians were made to work for the victory by the lowest-placed team left in the competition and there was little in it in the first half in front of 19,000 fans in Caen.
Attacking midfielder Ben Arfa has endured a frustrating time at PSG since moving from Nice in the summer and been a peripheral figure.
He was an unused substitute in Saturday's 4-1 mauling of Ligue 1 table-toppers Monaco in the final of the League Cup, but was a central figure against Avranches in a much-changed PSG line-up.
Top scorer Edinson Cavani was only on the bench and winger Angel Di Maria did not feature at all.
It left PSG struggling for rhythm in the first half but they took the lead on 35 minutes when Lucas Moura nudged the ball to Ben Arfa from a free-kick and he rifled the ball into the far corner from the edge of the box via a small deflection.
It was a timely reminder to PSG coach Unai Emery of the 30-year-old's quality.
Avranches failed to take a couple of decent chances at the start of the second half and Ben Arfa, whose career has been a series of brilliant highs and petulant lows, punished them with his second on 54 minutes.
Moura was again the unselfish provider and the Brazilian then got in on the act two minutes later for 3-0.
Javier Pastore sealed victory late on for 4-0.
Earlier, Cheikh Ndoye scored the winner in the second half as Angers saw off fellow Ligue 1 side Bordeaux 2-1 in the other quarter-final on the night.