Saido Berahino was left on the West Brom bench and James Morrison started in midfield as Pepe Mel's side showed a united front following reports of dressing room unrest in the wake of last weekend's 3-3 draw at Cardiff.
There was no late drama in Norfolk though, where a fine goal from Morgan Amalfitano on 16 minutes proved enough to settle what was for most a scrappy affair, although Norwich did twice hit the woodwork in the second half.
A second successive defeat for the Canaries - whose players had offered to refund the away supporters at Swansea last weekend - was met by loud boos at the final whistle, and leaves Chris Hughton's men still looking anxious over their shoulders ahead of games against Liverpool, Chelsea, Manchester United and Arsenal.
Norwich midfielder Alex Tettey had cracked in a brilliant 25-yard effort in the last match here against Sunderland, but the Norway international's radar was off range when trying his luck from a similar distance early on.
At the other end, an angled 20-yard drive from Graham Dorrans was well held by John Ruddy, before Amalfitano sliced his shot into the side-netting after a quick break down the West Brom right.
On 12 minutes, Johan Elmander crashed the ball high into the Barclay End after a deflected cross from Robert Snodgrass fell into his path on the edge of the West Brom penalty area.
It proved a costly miss, as the visitors went up the other end and swept into the lead on 16 minutes.
The ball was worked back inside from the left, and as full-back Martin Olsson slipped at the edge of the penalty area, Amalfitano skipped through before sliding a low shot across goal and into the far corner.
Norwich had not lost at Carrow Road in 2014 and needed a response to lift the silenced home faithful, clappers and all.
West Brom, though, remained comfortable in possession, determined to keep hold of their advantage.
It was almost 2-0 when a deep free-kick floated right through the Norwich penalty area and Jonas Olsson just failed to connect at the far post.
Norwich had Ruddy to thank when he blocked Matej Vydra's close-range effort after the visitors broke quickly down the left on a counter following a corner.
It was then the turn of the West Brom keeper to produce a fabulous stop after 38 minutes as he made a superb reaction save to tip away a glancing header from Elmander after Gary Hooper's flick-on.
Loud boos greeted the half-time whistle, leaving manager Hughton in no doubt of what was needed in his team-talk.
The Canaries boss sent the same XI out for the restart and did at least get something of a response as West Brom were forced on to the back foot.
On 57 minutes, the ball dropped to Hooper at the back of a crowded six-yard box and the former Celtic striker was unfortunate to see his angled drive hit the woodwork.
Foster then turned a clever 25-yard floated free-kick from Snodgrass up on to the crossbar as finally Norwich asked some questions of the West Brom rearguard.
Hughton made a positive change on 64 minutes as England Under-21 winger Nathan Redmond replaced Wes Hoolahan.
Snodgrass cut into the right side of the box after good hold-up play by Hooper, but could only slice his shot wide.
Berahino replaced Vydra on 71 minutes and the forward was soon in the action as he dragged a half-hearted effort wide following a quick break down the left.
Norwich sent on both Luciano Becchio and then Jonas Gutierrez as the hosts toiled for an equaliser.
West Brom midfielder Dorrans was replaced by Zoltan Gera, who then himself had to go off because of injury as Liam O'Neil came on for the final eight minutes.
Berahino waltzed into the Norwich box in stoppage time, but his near post shot was saved by Ruddy.