The Ligue 1 side recovered from a sluggish start to record a convincing win over its opponent, with the Croatian champion eliminated from the group stage
The visitors started the Group A encounter brightly, before Alex opened the scoring against the run of play after 16 minutes. Despite Zagreb maintaining pressure against the French runner-up, PSG eventually managed to undo the opposition with three second half goals.
All three were assisted by Zlatan Ibrahimovic, as Blaise Matuidi, Jeremy Menez and Guillaume Hoarau all scored to ensure that qualification is within sight for the capital club.
The hosts, expected to be re-invigorated after their shock 1-2 defeat to Saint-Etienne at the weekend, were too sloppy and disjointed in the opening proceedings, as Ante Cacic's men unexpectedly asserted their authority early on.
A defensive slip by Alex almost invited Marcelo Brozovic into an attacking chance, before Josip Pivaric latches onto a fine ball by Sammir on the left, and watched on as his fizzing low effort whisked past Salvatore Sirigu's goal by inches.
It took a little while for Les Parisiens to finally hit their stride, but even when they took the lead, they were not exactly out of second gear. From Jeremy Menez's corner, Zlatan Ibrahimovic helped on a pass towards center-back Alex, whose fantastic half-volley evaded the reach of Ivan Kelava after 16 minutes.
The goal sought to appease a fervent and demanding home faithful, who were already booing their side before the breakthrough, and it could've been 2-0 after young midfielder Adrien Rabiot fired over the bar after good work by Mohamed Sissoko.
Carlo Ancelotti's side toiled, and while its performance was not exactly that expected of a Champions League dark horse, it still managed to carve out opportunities as Ezequiel Lavezzi - back after a month out - slammed his effort in the side netting, despite a determined run.
The second half saw the French side step up its efforts and it was almost rewarded as Menez tapped in after a great pass by substitute Marco Verratti, with the offside flag curtailing its progress.
Dinamo was still threatening, and was close in breaking its Champions League duck as an enterprising Sime Vrsaljko produced a dipping cross, with Ante Rukavina's header flying narrowly over Sirigu's goal.
Subsequently, the Croatian champion was easily overridden in a matter of minutes after two brilliant moments of magic from Ibrahimovic. Firstly, Lavezzi's surging run towards the 31-year-old saw him provide Blaise Matuidi with a fine through-ball, as the midfielder turned past the goalkeeper for 2-0 on the hour.
Four minutes later, the game was settled as Ante Cacic's men realized their exit from the group stage. Ibrahimovic was once more the creative output as he fed Menez who subsequently cut in past a defender and fired the ball past Kelava for 3-0.
A clearly dazed opposition was still feeling the effects of its setback, and was unable to get back into the game. It was 4-0 with ten minutes to go after Matuidi set through Ibrahimovic, who slipped before still managing to pick out substitute Hoarau who produced the tap-in to eliminate Dinamo.
PSG resumes its Ligue 1 duties with a trip to champions Montpellier on Sunday, having amassed nine points in Group A. For Dinamo Zagreb, it will want to make a better impression of itself with its two remaining games now effectively dead rubbers.
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