Alan Pardew's men occupy the UEFA Europa League spot after a hard-fought win that follows triumphs over Chelsea, Tottenham and Norwich City.
Yoan Gouffran gave Newcastle a deserved lead 10 minutes before the break, nodding into an empty net following a poor clearance from Boaz Myhill.
West Brom started the second half in positive fashion and were rewarded when Chris Brunt levelled, the midfielder smashing a powerful effort past Tim Krul after Shane Long's glancing header found him free in the area.
Yet the visitors were ahead for just four minutes as Moussa Sissoko's swerving effort from distance beat Myhill all ends up to secure all three points for Pardew's side.
Long was retained in attack after his brace in Monday's 2-2 draw against Aston Villa.
Chris Brunt's free-kick tested Krul three minutes in, with the Dutchman forced to tip the ball wide, before Yohan Cabaye saw a long-range effort roll harmlessly wide of Myhill's right-hand post.
Newcastle grew into the game and saw Loic Remy's header deflected wide following good work on the right from Sissoko, while Shola Ameobi opted to shoot from distance rather than playing in his strike partner.
The hosts' pressure eventually paid off when Myhill could only parry a Cabaye corner skywards under pressure from Ameobi.
Sissoko's thunderous strike three minutes before the hour swiftly put Newcastle back on top and Debuchy should have put his side 3-1 ahead 15 minutes from time but instead shot straight at Myhill from the edge of the area.
The wasted opportunity was not to matter as Newcastle held on to leave West Brom, who introduced Zoltan Gera late on for his first appearance since January, with just one win in their last seven matches.
