It was a perfect night for Graham Potter's side, who dominated throughout.
Leandro Trossard opened the scoring on the stroke of half-time with a superb curling effort to follow up his match-winner against Southampton last weekend.
Ryan Fraser hit the post as the visitors started the second-half on the front foot but Danny Welbeck' s stunning strike - his third goal of the season - put Albion firmly in control.
Newcastle never looked like getting back into the game and Neal Maupay made sure of that when he finished off a slick team move, with a fine volley, for his first goal in ten games.
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Photos via Getty Images.
Ryan Fraser hit the post as the visitors started the second-half on the front foot but Danny Welbeck' s stunning strike - his third goal of the season - put Albion firmly in control.