Michael Owen scored twice as Newcastle made it four wins in six Premiership games with victory at the Hawthorns.
The England striker netted just seconds after half-time, showing great control to volley Charles N'Zogbia's cross high past Tomasz Kuszczak from six yards.
And he made it two with 12 minutes to go, reacting sharply to divert Kieron Dyer's low cross into the net.
Substitute Alan Shearer converted Peter Ramage's cross two minutes later as the Magpies moved up to 10th in the table.
Shearer, suffering with a hernia injury, had been dropped to Newcastle's bench by boss Graeme Souness.
But the match was crying out for his attacking ability during a woefully tepid first half.
The only real opening came in the 37th minute as Owen raced into the box and beat Tomasz Kuszczak to the ball, but the Polish keeper parried his shot.
But the second half was a very different affair, with Owen lighting up the match with a superb goal just 20 seconds after the restart.
The England striker nipped in front of Baggies defender Darren Moore to latch on to N'Zogbia's cross and send a beautifully controlled volley past Kuszczak from six yards.
West Brom's response was immediate as Robert Earnshaw made a threatening run, although Shay Given was equal to the Welshman's attempted chip.
Junichi Inamoto then sent in a powerful drive which Steven Taylor blocked, before Given produced a superb instinctive shot to deny Earnshaw from close range.
Newcastle hit back and Owen was denied a second goal when Inamoto headed his goalbound effort off the line.
The striker claimed the ball had crossed the line, but replays proved otherwise.
The match was open and Earnshaw again came close on the hour mark as his vicious low drive flew past the diving Given and just wide of the post.
Kuszczak then rode his luck as he raced outside his area to block as Owen broke - the striker reached the ball first and the keeper was fortunate he parried with his chest and not an arm as he spread himself to block.
Given was next in action as play once again swung to the other end, the Irishman tipping Earnshaw's curling effort away for a corner.
Shearer entered the fray on 65 minutes, although it was fellow substitute Dyer who made the first impact as he set up Owen's second.
He cut the ball back smartly from the touchline to the England striker who delicately diverted the ball high into the net.
And the Magpies made it comfortable two minutes later as Shearer pounced to divert Ramage's cross past Kuszczak from close range.
The two quick goals knocked the stuffing out of West Brom, and Bryan Robson was left to reflect on missed chances as the Baggies slumped to their fourth home defeat of the season.
West Brom striker Robert Earnshaw:
"We've conceded three goals in much the same way.
"We have to learn that. Michael Owen is very sharp and if you give him the space we did he will punish you.
"We created a few chances and were unlucky. But we've just got to forget about it as it is a disappointing result."
Newcastle manager Graeme Souness:
"Our football was good today and we scored good goals.
"Michael Owen is a proven goal scorer - he did not take part that much in the first half, but then within seconds he put us 1-0 up in the second half.
"At 1-0 Shay Given made a great save, had they scored maybe it would have been a very different game but as it turned out we won comfortably."
West Brom: Kuszczak, Scimeca, Curtis Davies, Moore, Clement, Greening (Horsfield 78), Watson, Inamoto, Carter, Kanu (Ellington 75), Earnshaw.
Subs Not Used: Hoult, Gaardsoe, Chaplow.
Newcastle: Given, Ramage, Boumsong (Bramble 79), Taylor, Babayaro, Solano, Parker, Emre, N'Zogbia (Dyer 71), Owen, Ameobi (Shearer 66).
Subs Not Used: Harper, Faye.
Goals: Owen 46, 78, Shearer 80.
Ref: H Webb (S Yorkshire).