Wayne Rooney converted from the penalty spot to give United a first-half lead before doubling their advantage at the start of the second period.
Juan Mata then came off the bench to score twice and seal the points for the champions.
Read Sports Mole's minute-by-minute report below to find out how all of the action unfolded at Old Trafford.
Fulham 2-2 Hull City
Stoke City 0-1 Tottenham Hotspur
Swansea City 4-1 Aston Villa
West Bromwich Albion 1-0 West Ham United
MAN UTD: LWDWLL
"During these four matches, I want to bring some positivity back, bring smiles to the faces. I want to see goals and tackles, I want to get the crowd up and I want to see the passion.
"It's going to be my philosophy - Man United's philosophy. I want the players to play with passion, speed, tempo, imagination - all the things I expect of a Man United player, but most of all, enjoy it. I want to see goals, I want see tackles, I want to see players taking players on."
"We're confident going into the game and we'll be confident going into the other two. If you're organised, you feel you're ready and you prepare the players in the right way, why not? We feel confident we can go and have a good go at it."
Bizarrely, a plane has just flown over Old Trafford with the message 'Thank U Moyes'. No joke.— Rob Dawson (@RobDawsonMEN) April 26, 2014
5 - Wayne Rooney has scored five goals in his last five Premier League appearances. Usual.— OptaJoe (@OptaJoe) April 26, 2014
11 - Manchester United have had more shots on target today than any previous Premier League game this season. Intent.— OptaJoe (@OptaJoe) April 26, 2014
ON THE DOUBLE Substitute Juan Mata celebrates the 1st of his two goals at Old Trafford. Man Utd 4-0 Norwich (88 min) pic.twitter.com/WdtjtDIJEI— Premier League (@premierleague) April 26, 2014