Despite the return of Zlatan Ibrahimovic and Marco Verratti from suspension, PSG headed into Tuesday's quarter-final second leg with a mountain to climb having lost the first leg at the Parc des Princes 3-1.
And the French champions never looked pulling off a remarkable comeback at Camp Nou, Neymar instead putting the tie beyond doubt with an excellent performance highlighted by two first-half goals.
The Brazil striker was the beneficiary of the sparkling creativity of Andres Iniesta as he netted an early opener, taking advantage of a fragile PSG defence without the services of injured captain Thiago Silva.
And a fine delivery from right-back Dani Alves, heavily linked with a transfer to PSG in the close-season, set Neymar up to head home his second - and his fifth in four games against PSG this season - 11 minutes before the break.
From there Luis Enrique's side proceeded to take their foot off the gas, coasting into the last four for the sixth time in the last seven seasons with a display that gives further credence to the idea that they could well win a Champions League, La Liga and Copa del Rey treble.
Barca needed just 14 minutes to break the deadlock thanks to a piece of brilliance from Iniesta.
The Spain star jinked his way beyond three players and played an expertly placed pass into the path of Neymar, who coolly rounded Salvatore Sirigu and tapped the ball into the empty net.
PSG responded well to going behind but only the reflexes of Sirigu prevented Barca from extending their lead soon after. The goalkeeper palmed a long-range strike from Dani Alves away and then kept out Neymar's header on the rebound.
But Sirigu could do nothing to stop Neymar from doubling his tally in the 34th minute as he was given the simple task of nodding home Dani Alves' excellent in-swinging right-wing cross.
Iniesta was withdrawn and replaced by Xavi at half-time and Barca did lose some of their attacking impetus in a low-key second half.
Yet they were rarely threatened by a PSG team, who never looked like they believed they could reverse last week's demoralising defeat at home.
Verratti lashed wide from the edge of the area and Ibrahimovic stung the palms of Barca keeper Marc-Andre ter Stegen, but that was all the visitors could muster as Barca - who nearly added a third through Lionel Messi in injury time - marched on in ominous fashion.
