Both sides began the game brightly with attacking football and efforts aplenty, most notably Salomon Rondon's ferocious 35-yard effort that rattled the Magpies' bar on 21 minutes.
The Baggies opened the scoring on the stroke of half time when Kieran Gibbs latched on to a pinpoint crossfield pass from Jonny Evans before crossing for Hal Robson-Kanu, who headed home from six yards out.
Newcastle halved the deficit three minutes later, going straight up the other end to win a corner, from which the unmarked Ciaran Clark headed home from point-blank range.
Rafael Benitez's charges continued to push forward in search of an equaliser and were rewarded in the 83rd minute as Matt Ritchie's driven free kick came off Evans and deflected into the West Brom net.
The result sees West Brom edge up to 16th place in the Premier League table, while Newcastle move up to 12th.
West Bromwich Albion (4-4-2): Foster; Nyom, Evans, Hegazi, Gibbs (McClean 80'); Livermore, Barry (Yacob 67'), Field (Krychowiak 84'); Phillips, Robson-Kanu, Rondon
Newcastle United (4-2-3-1): Darlow; Yedlin, Clark, Lejeune, Mbemba; Ritchie, Hayden (Shelvey 80'); Merino, Murphy (Aarons 64'), Perez; Joselu (Mitrovic 73')