The Spaniard lashed in from the edge of the penalty area after a misjudged free-kick from Ryan Taylor to cancel out Victor Anichebe's headed opener and claim a point
Having seen rivals Sunderland win 2-0 at Everton earlier on Saturday, John Carver's men approached the fixture under severe pressure to end a miserable run of form in front of their own fans at St James' Park.
West Brom increased the nerves among the home support when Victor Anichebe converted from Craig Gardner's free-kick in the 32nd minute.
But West Brom's advantage lasted only nine minutes as Ayoze Perez levelled for the hosts with a precise low strike.
Tony Pulis' West Brom were on the back foot for the majority of the second 45 minutes, yet would have taken all three points had Chris Brunt not struck the crossbar after 74 minutes.
The stalemate leaves Newcastle two points above 18th-placed Hull City - who lost 1-0 to relegated Burnley - with two games remaining.
Only the woodwork prevented West Brom from taking an eighth-minute lead as Youssouf Mulumbu headed against the upright from Craig Gardner's near-post corner.
Newcastle responded well, though, and would have gone ahead had Moussa Sissoko's effort not been cleared off the line by Joleon Lescott after Fabricio Coloccini had done well to nod Ryan Taylor's free-kick into the midfielder's path.
And Carver's men were immediately punished by Anichebe, who met Gardner's free-kick from the right with a well-executed header into the bottom-right corner.
Again Newcastle displayed good spirit and were rewarded for their determination by a superb finish from Perez.
The Spaniard controlled Taylor's short free-kick and fired a precise shot through a sea of bodies and beyond a stranded Boaz Myhill.
West Brom went close to taking the lead three minutes after the restart, Brunt shooting wide at the far post at the end of a well-worked move from the visitors.
Brunt was somehow denied again as his second attempt cannoned off the crossbar after seeing his initial effort blocked by Paul Dummett.
Substitute Saido Berahino was then twice thwarted by Tim Krul as West Brom threatened to deepen the gloom on Tyneside.
Still, Newcastle finished the match on the front foot, creating multiple chances in the closing minutes.
Remy Cabella shot over, Sissoko produced a diving save from Myhill and Sammy Ameobi went close with an overhead kick, but Newcastle could not find the goal that would have put them on the verge of survival.