West Brom started the game brightly, with Graham Dorrans only just missing the target with a powerful effort from the edge of the box following a quick passing move.
It took the Baggies until the 16th minute for them to take the lead, and it was Morgan who scores his second goal in as many games with a low strike from 18 yards after taking advantage of Martin Olsson's slip.
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The Canaries were inches away from equalising in the early stages of the second half when Gary Hooper fired a loose ball against the crossbar from inside the box.
Norwich pushed for the equaliser until the final whistle, but they were fortunate not to lose by a wider margin when Saido Berahino's powerful strike was stopped by Ruddy.
The Baggies managed to hold off the hosts in the closing stages to secure the victory and pile more pressure on Hughton.