Barca had not conceded a goal this season but David Luiz, Marco Verrati and Blaise Matuidi all punctured their defence to give the French champions three points.
Luiz put the home side ahead in the 10th minute only for Lionel Messi to equalise two minutes later at the end of a sharp move before Verrati's 26th-minute header put PSG in front again.
Matuidi caught the Barca defence snoozing again early in the second half and although Neymar pulled one back with a fine goal almost immediately PSG held firm.
PSG lead Group F with four points, with Barca on three and Ajax Amsterdam third two points after drawing 1-1 with APOEL.
"There is a lot of satisfaction because we were going through a rough patch," PSG coach Laurent Blanc told a news conference.
"Even if some players played a great match, what I keep in mind is the collective performance of the team."
Barca coach Luis Enrique said his side had woken up in the last 25 minutes.
"In the last 25 minutes we could play our game and we could have equalised, although I'm not saying we did not deserve to lose," he told a news conference.
"I was not surprised by the level of PSG without Ibrahimovic, we know the potential of this team, they are Champions League contenders and won their league."
ELECTRIC NIGHT
With Jay Z, Beyonce and David Beckham watching from the stands on an electric night at the Parc des Princes, PSG looked transformed from the side that had drawn six of their opening nine games of the season.
They tore into a Barca side that had kept clean sheets in their first seven games in all competitions, making the Catalans look fragile at the back.
Talisman striker Ibrahimovic was ruled out of the tie with a heel injury, but PSG made up for his absence with Javier Pastore's brilliance and Verratti's grit.
PSG were rewarded for their early aggression when Luiz scored with a low shot on the turn from a Lucas free kick.
Barca quickly recovered from the shock of conceding their first goal of the season with Messi sweeping the ball past Salvatore Sirigu after a fine one-two with Andres Iniesta, who was making his 100th Champions Leaque appearance.
Edinson Cavani came close to making it 2-1 for PSG but his rising shot from outside the box sailed just high.
In an entertaining first half, the visitors also had a clear chance when Messi's snap shot from inside the area was parried away by Sirigu in spectacular fashion.
Neymar was inches away from converting Messi's brilliant chip with a first-time lob but it went just wide.
It was Barca, however, who cracked again when an unmarked Verratti headed home from Thiago Motta's corner.
Matuidi made it 3-1 nine minutes into the second half, beating Marc-Andre ter Stegen from close range after escaping Daniel Alves at the far post.
On a high-octane night Neymar slotted a delightful shot in off the far post two minutes later but the expected Barca onslaught never really materialised despite late pressure.
Not even the 69th-minute introduction of Xavi, on for Ivan Rakitic, for a record 143rd appearance in the Champions League could earn Barca an equaliser.
Xavi surpassed the previous record he held with former Real Madrid and Schalke 04 striker Raul.
(Reporting by Julien Pretot; Editing by Martyn Herman)
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