West Ham were expected to provide a stern test after a run of five games without defeat, but despite Morgan substitute Amalfitano hitting the post late on, Sam Allardyce's team were well beaten in what was the London rivals' 100th encounter.
"We played a very good game against a very difficult opponent. When we scored, we had the game always under control," Mourinho told Sky Sports.
"I am really happy. We are doing very well."
City were again without injured strikers Sergio Aguero and Edin Dzeko at a snow-splattered Hawthorns, but they made short work of West Brom regardless to register a ninth consecutive victory.
Fernando punished an error by goalkeeper Ben Foster to put City ahead in the eighth minute, with a Yaya Toure penalty and a David Silva goal extending the visitors' lead before Brown Ideye scored a late consolation.
Manchester United returned to winning ways following last weekend's 1-1 draw at Aston Villa by sinking Newcastle at Old Trafford.
Rooney broke the deadlock in the 23rd minute, tapping in after a sliding Radamel Falco steered Juan Mata's pass across goal, and added a second goal 13 minutes later with an assured finish from Mata's pass.
The United captain, who played in midfield again, teed up Robin van Persie to head home the hosts' third goal eight minutes into the second half, before Papiss Cisse replied with an excellent late penalty.
Southampton moved into the top four, three points below United, by winning 3-1 at Crystal Palace, who slipped into the relegation zone.
Sadio Mane rounded Allan McGregor to put the visitors ahead in the 17th minute, with quick-fire goals by defenders Ryan Bertrand and Toby Alderweireld making the game safe before Scott Dann scored late on.
Tottenham also exploited West Ham's defeat by winning 2-1 at bottom club Leicester City.
Christian Eriksen's 71st-minute free-kick secured victory after Leonardo Ulloa had cancelled out Harry Kane's first-minute opener for Spurs.
Swansea climbed as well, moving to within four points of the Champions League places by beating Aston Villa 1-0 thanks to Gylfi Sigurdsson's curling 13th-minute free-kick.
Liverpool ended a run of three games without victory by winning 1-0 at Burnley through Raheem Sterling's first league goal for September.
Liverpool lost goalkeeper Brad Jones to injury, which saw the dropped Simon Mignolet summoned from the bench, and Merseyside rivals Everton also lost their goalkeeper in a 1-0 defeat at home to Stoke City.
Tim Howard was forced off in the second half at Goodison Park, after Bojan Krkic had scored the game's only goal from the penalty spot in the 38th minute.
In the day's other game, Gaston Ramirez scored one and made another as Hull City escaped from the bottom three by coming from behind to win 3-1 at Sunderland.
Adam Johnson put Sunderland ahead in the first minute, but Ramirez equalised with a speculative shot and then teed up James Chester before Nikica Jelavic added a third in injury time.
AFP gjw
-AAP
