After a goalless first half at the Parc des Princes, Ibrahimovic opened the scoring on 63 minutes when he converted Lucas's cross from close range.
The Swede added to his tally and effectively made the game safe when Serge Aurier's cross from the right found him in acres of space on the penalty spot to finish left footed.
Adrien Rabiot scored from a Maxwell cross to complete the rout with 15 minutes left.
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PSG have not lost in any competition since defeat by Real Madrid in the Champions League in early November and they have gone 21 matches with only one drawn one game.
St Etienne needed extra time to beat Troyes 2-1 away as did Nantes, who reached the last eight with a 4-3 win at Girondins Bordeaux.
FC Lorient thrashed fourth tier Sarre Union 4-0.
(Writing by Toby Davis in London; editing by Ed Osmond)
