With David Luiz, Thiago Motta and Edinson Cavani sidelined and a Coupe de la Ligue final with Bastia as well as a UEFA Champions League tie with Barcelona on the horizon, PSG coach Blanc named a much-changed side for the last-four clash.
Still the Ligue 1 leaders had enough to see off a stern test from Christophe Galtier's side, Ibrahimovic opening the scoring with a landmark goal from the penalty spot at the Parc des Princes.
The talismanic striker converted after Francois Clerc had harshly been adjudged to have pulled down Ezequiel Lavezzi.
Romain Hamouma ensured PSG's lead short-lived when the winger levelled matters by turning home from a Yohan Mollo set-piece, only for Lavezzi to restore the hosts' advantage after the break.
Ibrahimovic then put on a late finishing masterclass, stylishly adding PSG's third in the 81st minute before sweeping home in injury time to take his tally to 102 for the French champions - who face Auxerre in the final on May 30.
PSG started on the front foot and Lavezzi was twice denied by Saint-Etienne goalkeeper Stephane Ruffier in the first 15 minutes.
Ruffier did well to punch away a Lavezzi volley after the Argentinian forward had latched on to an Ibrahimovic header and again thwarted the former Napoli man at the near post following more good work from the Sweden striker.
But the hosts' pressure told in the 20th minute when Lavezzi broke through the Saint-Etienne defence before appearing to go down easily under the challenge of Clerc.
Referee Fredy Fautrel showed no hesitation in pointing to the spot and Ibrahimovic coolly slotted the penalty into the bottom-left corner to reach the century mark.
Yet PSG's lead lasted all of four minutes, as Hamouma levelled by glancing home Mollo's left-wing free-kick.
Blanc's men would have fallen behind if not for the reflexes of Nicolas Douchez, who came in for first-choice goalkeeper Salvatore Sirigu as one of six PSG changes.
Douchez used his legs to keep out former PSG striker Mevlut Erding's shot following a poor Gregory van der Wiel back-pass and turned Loic Perrin's header from the resulting corner over the crossbar.
Ibrahimovic forced Ruffier into another save with a low free-kick in the 35th minute and, after ramping up the pressure following the restart, PSG re-established command as Lavezzi got the goal his impressive display merited.
Lavezzi met a cross from compatriot Javier Pastore with an expertly placed header into the bottom-right corner on the hour-mark.
Ibrahimovic struck the post in the 71st minute following a quick PSG counter, but 10 minutes later he did add a third with a moment of class.
Substitute Blaise Matuidi played Ibrahimovic in and he cleverly flicked the ball round Ruffier then tapped into the empty net. The former Barcelona man then capped things off by claiming his hat-trick with a powerful strike just inside the near post in stoppage time.
