Ibrahimovic bundled in the opening goal with his chest just past the hour at the Parc des Princes and the Sweden international added a second soon after. Adrien Rabiot wrapped up the victory 15 minutes from time.
PSG are attempting to repeat last season's clean sweep of all three domestic competitions. They are 24 points clear at the top of the French first division and also in the final of the French League Cup.
In Wednesday night's other match, Nantes scored twice in the last five minutes of extra-time to claim a 4-3 victory at Bordeaux. The United States international Alejandro Bedoya grabbed the winner in the 118th minute.
Saint-Etienne also needed extra-time to squeeze past Troyes 2-1, but there was no chance of giant killing as first division Lorient thrashed fourth division Sarre-Union 4-0.
Just hours after PSG progressed to the last eight, the club hierarchy announced that coach Laurent Blanc had extended his contract until 2018.
Blanc's current deal runs out at the end of the season and PSG's Qatari owners have shown faith in the former Bordeaux boss before the last 16 clash against Chelsea in the Uefa Champions League, a trophy PSG's money men have placed as a priority.
"I'm very happy, also for my staff," said 50-year-old Blanc. "A coach is nothing without his staff. For us, continuing the adventure is a show of faith but also a big responsibility. The club has ambitions both nationally and in Europe, and we'll do all we can to reach those objectives."
Blanc, who took over in 2013 after two years as boss of the France national team, has guided PSG to two of their three consecutive Ligue 1 titles. He said winning Europe's most prestigious club competition was a feasible objective. "We'll get there," said the former France international. "We're ready. We're aware that we're at a big club where expectations are very high."
PSG have not lost a game in domestic competitions for seven months. They are hunting their first Champions League title after falling at the quarter-final stage for the past three seasons.
PSG owner Nasser Al-Khelaifi said he was proud and happy that Blanc had agreed to continue in the French capital. "It was important to us that he be a continuing part of Paris Saint-Germain's plans," he said. "He has obtained excellent results since his arrival. He has already won eight trophies with us, which is quite simply formidable. Also, I like our team's playing style, a style that he has instilled."