Zlatan Ibrahimovic gave PSG a 15th-minute lead at Camp Nou, but goals from Lionel Messi and Neymar made it 2-1 at the interval.
The third member of Barca's menacing attacking trio - Luis Suarez - rounded off the scoring late on to subject the French champions to their first defeat of the season in all competitions.
The result saw PSG slip to second in Group F, meaning they are likely to face a tougher test in the last 16 than if they had remained top.
And former Chelsea man David Luiz admitted PSG were taken by surprise by a slight tactical switch from Barca coach Luis Enrique that saw the hosts line up in a 3-4-3 formation.
"I think that Barcelona are a great side, they've played very well, with a diamond in the middle of the park in order to have more possession," he said. "This surprised us.
"Barca have some of the best forwards in the world, all three of them are top quality and they all scored.
"We have to be ready to play against any team if we want to win the tournament, even if we'd have preferred to play the second leg at home."
PSG will face Atletico Madrid, Real Madrid, Borussia Dortmund, Bayern Munich, Chelsea or Porto in the next round.
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