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After being handed a rare start by head coach Tony Pulis, Victor Anichebe was in the thick of the action during the early stages and almost gave his side a third-minute lead, only for his effort to be cleared off the line by Fabricio Coloccini.
James Morrison also had a shot saved by Newcastle goalkeeper Karl Darlow - playing in place of Rob Elliot - before up the other end, Boaz Myhill needed to be alert to parry away a Georginio Wijnaldum strike.
Heading into the fixture, West Brom possessed one of the worst home records in the Premier League but they pushed forward relentlessly before the half-hour mark, with Morrison shooting wide of the post and Fletcher seeing a goalbound effort blocked.
Fletcher would be denied twice more before the half-time whistle, but soon after the restart, it was Newcastle who should have edged in front, with both Paul Dummett and Coloccini hitting the woodwork during the same sequence in play.
However, as the match drew to a close, the Baggies started to get back on top, and moments after Anichebe headed against the crossbar, Fletcher got on the end of Claudio Yacob's cross to send his header past Darlow.
Substitute Saido Berahino almost made it two shortly afterwards, but despite his powerful drive being saved by Darlow, West Brom comfortably held on to move six points clear of the relegation zone, with Newcastle dropping two points from safety.