The Baggies had to settle for a draw after Ayoze Perez's equaliser nine minutes before the break, after Anichebe had put the Baggies ahead.
But the point, combined with Hull's defeat to Burnley, meant the Baggies were safe in the top flight for next season.
The first half was a dreadful spectacle with Albion having the only genuine chance in the opening half-hour.
That fell to Craig Dawson, who rose highest to meet an early Craig Gardner corner and send a thudding header against the post, with Youssouf Mulumbu's follow-up charged down.
Newcastle had a couple of half-chances when Paul Dummett headed Ryan Taylor's free-kick over and then when Taylor blasted just wide from 25 yards.
And they went closer just before the half-hour when Moussa Sissoko's effort was cleared off the line by Joleon Lescott after the forward's initial effort had struck Jonas Olsson.
But it was the Baggies who went ahead on 32 minutes when Jonas Gutierrez fouled Dawson and Gardner's free-kick was headed home perfectly by Anichebe.
The lead lasted just nine minutes, however, before some sloppy defending handed the home side an equaliser.
The Baggies stood still and failed to clear a Taylor free-kick, allowing Perez to fire home from 15 yards.
Early in the second half a big chance went begging for the Baggies.
Anichebe did well to hold the ball up and feed Fletcher, whose left-wing cross found Gardner arriving at the far post.
But the midfielder fired wide of the target when he should have at least tested keeper Tim Krul.
The game livened up a little in the closing stages and Albion went agonisingly close.
Goals: Anichebe 32, Perez 41.
Newcastle (4-3-3): Krul, Anita (Abeid 90), Coloccini, Dummett, Gutierrez, Cissoko, Taylor, Colback, Perez (Ameobi 85), Riviere (Cisse 69), Cabella.
Substitutes not used: Woodman (GK), Gouffran, Aarons, Satka.
West Brom (4-5-1): Myhill, Dawson, McAuley, Olsson, Lescott, Gardner (Berahino 69), Mulumbu (Morrison 55), Yacob, Fletcher, Brunt, Anichebe (McManaman 78).
Substitutes not used: Rose (GK), Wisdom, Baird, Ideye.
Referee: Chris Foy (Merseyside)
Chris Brunt's header from a Dawson cross cleared off the line by Dummett before Brunt and substitute Saido Berahino combined to force the rebound onto the crossbar.
And Berahino then had an effort saved by Krul after being fed well by Anichebe.
Berahino had another opening when he raced onto a lofted pass from Brunt, but again he fired too close to Krul.
In stoppage time, Myhill pulled off a smart save to deny Sissoko and substitute Sammy Ameobi sent an overhead kick over the crossbar.

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