Norwich City hot shots Josh Sargent and Jon Rowe produced the goods as the Canaries kept themselves firmly in the play-off picture.
Goals in each half made it five league and cup wins without defeat for City, who sit two places and two points behind sixth-placed Coventry City.
They took the lead on 13 minutes when Kenny McLean brought the ball out of defence to the halfway line, saw Sargent in the right channel and the striker headed goalwards before firing home, Palmer unable to hold his shot.
It was a goal which prompted a good spell, for the Canaries, who passed the ball well at times, and with purpose.
Jon Rowe was twice denied by keeper Alex Palmer, Borja Sainz lobbed wide and Dimi Giannoulis fired high and wide when well positioned.
Angus Gunn was perhaps fortunate not to concede a penalty when he tackled Darnell Furlong, as City suddenly got an attack of the nerves.
The Baggies were on the front foot for large parts of the second half, but City's backline - well supported by Borja Sainz and Rowe - held firm as the hosts managed the game out to perrfection.
The lead was doubled on 71 minutes when City broke well and Giannoulis slid the ball in to the path of Rowe who knocked it home from six yards for his 12th Championship goal of a brilliant season.
NORWICH CITY:
Substitutes:
12 Long (GK)
8 Liam Gibbs
11 Adam Idah (Barnes 80)
15 Sam McCallum (Giannoulis 90)
16 Christian Fassnacht (Sainz 64)
19 Jacob Sorensen
25 Onel Hernandez (Rowe 90)
26 Marcelino Nunez (Sargent 64)
35 Kellen Fisher
Head coach: David Wagner
Bookings: Stacey
Goals: Sargent 13, Rowe 71
WEST BROM
Substitutes:
33 Josh Griffiths (GK)
12 Daryl Dike (Thomas-Asante 69)
14 Nathaniel Chalobah (Yokuslu 36)
15 Erik Pieters
17 Andreas Weimann (Reach 46)
26 Pipa (Furlong 83)
32 Jovan Malcolm
36 Caleb Taylor (Bartley 83)
37 Harry Whitwell
Head coach: Carlos Corberan
Bookings: Furlong, Wallace
Goals:
KEY MOMENTS
4 - Gibson does well to flick the ball away with his head from a good Townsend cross.
7 - Swift fires a free-kick wide of Gunn's right post
10 - Good tackle in side his own area by Gibson on Thomas-Asante - might well have prevented a goal.
12 - Sara drills a low shot from the left, but it's an easy gather for Palmer.
13 - GOAL SARGENT - McLean brings the ball out of defence, gets to the halfway line and sees Sargent in the right channel and the striker head goalwards before firing home, Palmer unable to hold his shot.
26 - Sargent shot blocked by Wallace, loose ball falls to Sainz who lobs wide.
30 - Good passing attack by Norwich ends with Rowe forcing a smart save from Palmer.
31 - More good stuff from City, this time a better save by the keeper from Rowe's left-footer.
34 - Good break by McLean down the right, ends with Giannoulis blasting a shot wide.
38 - Gunn comes out of his goal to tackle Furlong - West Brom appeal for a penalty, but nothing is given.
45 - Lovely left foot free-kick by Sara - ball dips and lands on top of the net.
45 - Thomas-Asante has the ball in the net but uses his arm and the whistle blows.
HT: City 1 West Brom 0
49 - Giannoulis does well to deny Swift.
51 - Swift fires a shot inches wide of Gunn's right post
54 - Rowe on the stretch heads McLean's cross over.
66 - Thomas-Asante shot on the turn deflected behind by Gibson.
68 - Swift ball into the area, Thomas-Asante guides it on with his head but Gunn does well to save.
71 - GOAL NORWICH - Rowe doubles the lead after a good break down the right by Stacey. The ball is moved infield to Sara, who lays it off left to Giannoulis, who slides it into the path of Rowe, who does the rest from six yards.
75 - Free header for Baggies sub Dike but it is too close to Gunn, who saves comfortably.
77 - Dike skews one wide.
81 - Rowe twists and turns in the area before firing goalwards - Palmer turns it away for a corner.
88 - Weimann fires wide.
90 - Sub McCallum does really well to head the ball out for a corner, under pressure from Dike.
FT: Canaries 2 West Brom 0
PLAYER RATINGS
Gunn 6, Stacey 7, Duffy 6, Gibson 7, Giannoulis 7, Sara 8, McLean 7, Rowe 8, Barnes 7, Sainz 8, Sargent 7. Subs: Idah 6, McCallum 6, Fassnacht 6, Hernandez 6, Nunez 6.
MATCH STATISTICS
Possession: 40%-60%
Shots: 13-15
On target: 6-3
Corners: 2-6
Fouls: 9-10
Added time: 4 mins/5 mins
Att: 25,800
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