It was the second meeting between the two teams in a matter of days, with PSG winning 2-0 in the league fixture on Sunday.
That match saw David Beckham make his debut from the bench for the capital club, and on Wednesday night he made his first start after joining on a five-month deal last month.
But if the pre-match headlines had focused on the former England international, Ibrahimovic turned the attention his way with the opening goal after 34 minutes from Clement Chantome's pass.
Marseille were not without their chances and the match became heated at times as they pushed for an equaliser.
However, Sweden international Ibrahimovic made sure of PSG's place in the last eight with a 65th-minute penalty after he was brought down in the area by left-back Jeremy Morel.
Beckham's appearance lasted 86 minutes and he left to warm applause to be replaced by Christophe Jallet.
Bordeaux also progressed through to the quarter-finals but it was a far less comfortable affair for the Ligue 1 club, who beat fourth-tier side Raon-L'Etape in a penalty shootout.
The scores were 1-1 at the end of 90 minutes after Ludovic Obraniak's 59th-minute opener was cancelled out by Jean-Philippe Dje six minutes later.
Amara Keita then gave Raon the edge in extra-time but Cheick Diabate replied from the penalty spot to take the match into a shootout.
Les Girondins were successful with all of their spot-kicks but Tresor Nyamwisi missed for the home side to deny them a famous win.
Nancy also survived a scare against amateur opposition, seeing off Minguettes 2-0 after extra-time. Having failed to score during normal time, goals from Benjamin Moukandjo Bile (106) and Thomas Ayasse (120) eventually saw Nancy through to the next round.
Lorient had few worries booking their place in the last eight, seeing off Ligue 1 rivals Brest 3-0 with second-half goals from Jeremie Aliadiere (two) and Bruno Ecuele Manga.