Newcastle were straight onto the front foot, forcing a free-kick and a corner, and getting a shot on target in the first three minutes alone.
But in only their second attack, Barca took the lead, with Raphinha passing the ball into the net after a lightning-fast move upfield.
With the hosts then in the ascendancy, a second goal seemed inevitable, but some lax defending allowed Lewis Hall to send in a cross for Anthony Elanga, and he fired past Joan Garcia.
Just two minutes later, Joelinton hauled back Lamine Yamal, and from the resulting free-kick, Marc Bernal was left unmarked in the six-yard box to put the hosts back in front.
The game then settled down, but as the half hour approached, a ridiculous attempt at a backheeled clearance by Lamine saw Barca punished. Hall and Harvey Barnes combined to play in Elanga at the far post, with the winger making no mistake as he grabbed his second goal of the night.
The hosts went close a couple more times before a Kieran Trippier foul on Raphinha in the box ended with Lamine Yamal burying a stoppage-time penalty into the bottom-right corner, despite Aaron Ramsdale guessing correctly.
The hosts were much more purposeful at the beginning of the second half, as Newcastle found it difficult to get out of their own half.
And on 52 minutes, Fermin Lopez finished off a sweeping Barca move that went from back-to-front in seconds, giving the Catalan giants a two-goal cushion for the first time in the match.
Shortly after, Robert Lewandowski’s towering header from a Raphinha corner seemingly took the tie away from the visitors once and for all, and the Polish international added a sixth on the hour with a fine low strike.
Newcastle then shot themselves in the foot when Malick Thiaw’s attempted square ball across his own box landed right at the feet of Raphinha.
A simple right-footed finish gave Barça a seventh on the night, and the result means that the Blaugranes progress after a 16th win in 17 Round of 16 ties.
Meanwhile, Newcastle’s six-game unbeaten run in the UCL (W3, D3) comes to an ignominious end.
Flashscore Man of the Match: Raphinha (Barcelona)
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