Angel Di Maria scored twice for the French champions on his 29th birthday at the Parc des Princes, while Julian Draxler and Edinson Cavani -- on his 30th birthday -- were also on target in a stunning home performance.
The result leaves PSG on the brink of a place in the quarter-finals for the fifth season in succession, while Barcelona are staring at their earliest exit since losing to Liverpool in the last 16 in 2007.
"It is difficult to explain. They were superior to us from the start," admitted Luis Enrique.
"There was a 15-minute spell in the first half in which we were on top, but otherwise PSG attacked quickly on the break and created a lot of chances.
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"It was a disastrous night for us. They were completely superior. There is not much more to say."
Di Maria curled in his second and the home side's third 10 minutes after half-time before Cavani completed the rout with his 34th goal of the campaign in the 71st minute.
"PSG did what we expected them to do and produced their best version and we were at our poorest," the Barcelona coach added. "It's extremely difficult for us now but we go back to our stadium and really we need a heroic performance but why not dream?
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