Saint-Etienne 0 Paris Saint-Germain 1: Ibrahimovic puts holders through
PSG talisman Ibrahimovic chested home Lucas Moura's cross 18 minutes from time at Stade Geoffroy-Guichard on Tuesday to edge the holders into the last four.
Saint-Etienne were not convinced the ball had crossed the line, but replays showed goalkeeper Stephane Ruffier had not managed to claw the ball back in time and play was then suspended after objects were thrown onto the pitch by the home supporters.
There was very little between the two sides, but PSG held on for a morale-boosting victory just three days after they squandered a two-goal lead to lose 4-2 at Bastia in Ligue 1.
That defeat left Laurent Blanc's champions fourth in the table, with Saint-Etienne moving above them into the third spot, but the hosts were unable to heap more misery on the Parisian giants as they slipped to their first home loss since October.
Blanc - who once again omitted Edinson Cavani and Ezequiel Lavezzi for disciplinary reasons - backed PSG to respond after caving in at Bastia, and they made a bright start.
Ibrahimovic, who scored a hat-trick in a 5-0 hammering of Saint-Etienne back in August, tried his luck with a well-struck free-kick that was palmed away by Ruffier eight minutes in.
But in-form Saint-Etienne, who had lost just one of their last 17 games going into this match, grew into the contest and Moustapha Bayal Sall rose to meet a corner from the right with a towering header that was cleared off the line by Marco Verratti.
Italian midfielder Verratti then embarked on a positive run into the hosts' penalty area, but blazed his shot high and wide - his effort in keeping with a first half that lacked quality in the final third at both ends.
Substitute Benjamin Corgnet wasted a golden opportunity to put Saint-Etienne in front on the hour-mark, but shot just wide after ghosting into the box unmarked.
Lucas then broke the offside trap and rounded Ruffier, but was unable to tuck the ball into the empty net from a tight angle.
The Brazilian made amends 18 minutes from time, though, whipping in an inviting cross that Ibrahimovic chested over the line despite the best efforts of Ruffier.
Referee Said Ennjimi then suspended the game as objects were hurled onto the pitch from behind the goal, but play resumed after Saint-Etienne boss Christophe Galtier urged fans to calm down.
Blaise Matuidi ought to have doubled the visitors' lead when he was sent clear and his attempt was kept out by Ruffier, before PSG keeper Nicolas Douchez produced an outstanding reflex save to keep out Ricky van Wolfswinkel's header four minutes from time to ensure PSG edged through to the last four.