Rashford's brace was too much for Newcastle, with Anthony Gordon's late goal coming too late.
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The Manchester United loanee said afterwards: "It is going good, I am learning a new way of football and it's making me a better player.
"It is an amazing experience to play for Barcelona and we want to win as much as possible. It is refreshing to play with these guys.
"The ambition is to win the Champions League, nothing else is on our minds. It is going to be tough, we know that."
Rashford, on his second goal, added: "It's up there (with the best I've scored). I liked the first one too – it was a good team goal. I'm just happy I can contribute and help the team. We knew how hard it was going to be tonight."