Elias Sorensen's first goal of the season put the Magpies in front at half time at Little Benton. Adam Wilson was fouled and the Danish forward fired the resulting penalty beyond Adam Przybek.
Thomas Allan and Kieren Aplin had chances to add to United's advantage but the Baggies equalised shortly before the hour mark through Jamie Souf.
Morgan Rogers then put the visitors ahead before, a minute later, Nick Phillips beat Otto Huuhtanen via the underside of the crossbar.
Two minutes from time, Rogers scored his second and Albion's fourth.
United take a break from league action next weekend as they entertain Brighton in the Under-18 Premier League Cup on Saturday (kick-off 11am).
Newcastle United Under-18s: Otto Huuhtanen, Sam Joyce, Kieren Aplin, Jack Young, Lewis Cass, Kelland Watts, Adam Wilson, Mace Goodridge, Elias Sorensen (Thomas Cole 78), Thomas Allan, Deese Kasinga (Kurtis Russell 78)Subs not used: Isaac Gamblin, Dan Langley, Ryan Barrett