The victory came in no small thanks to Swedish striker Zlatan Ibrahimovic, who assisted on all four PSG goals, drawing praise from trainer Carlo Ancelotti.
"Zlatan is a great player because he also plays for his team-mates, he scores and helps others to do so," Ancelotti said following the match.
"I am very happy because he is 100 percent involved in the team, he is a fantastic player and an outstanding character."
Goals from Alex, Blaise Matuidi, Jeremy Menez and Guillaume Hoarau guided the Parisians to a third win from four matches in Group A, lifting them onto nine points, one behind leaders Porto, who were held to a goalless draw at Dynamo Kiev.
The Ukrainian outfit lie third on four points, while defeat for Zagreb extended their barren group phase run to 10 matches, eliminating them from this year's competition and leaving them as the only team yet to score.
Ibrahimovic, who was a constant thorn in the visitors' defence as he set up all four goals, told Canal+ after the match: "They had a good first chance against us. (But) we took our chances.
"It's always easier, when you're ahead and when you have more space. We could have scored two more goals, but 4-0 is a good result."
Carlo Ancelotti made five changes from the side that succumbed at home to Saint-Etienne on Saturday -- a result that snapped the Parisians' unbeaten league start -- with Ezequiel Lavezzi a surprise inclusion following his return to fitness.
17-year-old Adrien Rabiot was also handed a European debut with the Italian's midfield options decimated by injuries, while Alex was preferred to Mamadou Sakho in the heart of defence with Christophe Jallet slotting in for Gregory Van der Wiel on the right.
PSG were fortunate not to fall a goal behind, surviving an early scare as Josip Pivaric's angled shot flashed narrowly wide of the far post.
Menez then should have forced a save from goalkeeper Ivan Kelava after Lavezzi's clever pass put him clean through, but the Frenchman, with one eye on the linesman's flag, miscontrolled allowing the keeper to claim.
But PSG soon found a breakthrough after 16 minutes as Alex swept home Ibrahimovic's cross after the Swede exchanged passes with Lavezzi from a short corner.
Thiago Silva was denied a second as Kelava somehow corraled his close-range header after the Brazlian had latched on to Mohamed Sissoko's initial effort.
The Dinamo keeper then used his legs to intercept a pass destined for Ibrahimovic, who was unmarked at the far post.
Marco Verratti was introduced after the restart as PSG sought to turn their superior possession into something more meaningful.
Zagreb's best chance fell to Ante Rukavina as he climbed well to meet Sime Vrsaljko's ball in from the right, but his powerful header zipped over the crossbar.
The club from the French capital started to turn the screw and doubled their lead on 61 minutes as a delightful pass from Ibrahimovic picked out Matuidi, who calmly slotted beyond Kelava.
Menez, who scored in the corresponding fixture a fortnight ago, repeated the feat as he added a third four minutes later.
The France international collected the ball on the edge of the box before cutting inside, leaving Ante Puljic seated on the turf, and showed great composure as he slipped the ball under Kelava.
Menez then squandered a glorious opportunity to net a fourth, as he failed to get a shot off after trying to round the keeper.
But PSG weren't finished as Ibrahimovic broke into the Dinamo box, and despite losing his balance under pressure from Kelava, managed to flick the ball to Hoarau who steered the ball into the unguarded net.