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.
Matej Vydra had an opportunity to double West Brom's lead after combining well with Stephane Sessegnon, but the striker was denied by John Ruddy's save.
Norwich struggled to create many clear opportunities in the first half, but they could have been level when Johan Elmander's flicked header was pushed away by Ben Foster.
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.
Chris Hughton's side were denied by the woodwork once again as Robert Snodgrass saw a free kick tipped against the bar by Foster.
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.
Source: www.sportsmole.co.uk
