Fermin Lopez and Joao Cancelo put Barcelona on their way at Estadi de Montjuic, but the hosts were made to work hard by the Italian side who pulled one back through Amir Rrahmani.
Following an brisk opening, Barcelona landed a mighty one-two punch on Napoli with two goals in three minutes.
First, 20 year-old midfielder Lopez took his chance to impress on the big stage as he stroked home a side-footed finish on 15 minutes after Lewandowski dummied Raphinha’s low cross.
Former Leeds winger Raphinha was also at the centre of Barcelona’s second, leading a counter-attack and curling a shot off the post before Manchester City loanee Cancelo scored from the rebound.
Barcelona however ceded momentum, and Napoli pulled one back on the half hour when Kosovan centre-back Rrahmani ventured forward to slot past Marc-Andre ter Stegen following a cutback from the right.
Napoli pushed hard for an equaliser, and missed their best chance with 10 minutes remaining as Jesper Lindstrom sent a free header wide from seven yards.
But they eventually came up short as Barcelona sealed a win for the first time in five Champions League knockout ties when Lewandowski tapped home after being set up by slick play from Sergi Roberto.
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