The forward struck first from the penalty spot after Danny Welbeck was felled in the area and he completed his brace after the interval with a rasping effort from outside the Norwich area.
Substitute Juan Mata got on the scoresheet just three minutes after his introduction on the hour mark and he grabbed another with 17 minutes remaining.Ashley Young, Tom Cleverley, Phil Jones and Michael Carrick all featured in United's biggest home win of the season.
Elsewhere, England striker Rickie Lambert inspired Southampton to a 2-0 victory over Champions League-chasing Everton in the Premier League's early kick-off.
Lambert, who scored with his first touch in an England shirt against Scotland at Wembley Stadium in August, produced a dangerous cross from the left-hand side in the opening minute which Everton defender Antolin Alcaraz inadvertently headed into his own net.
The Toffees' top-four aspirations were left in tatters midway through the first period when Seamus Coleman scored their second own goal of the game, heading Nathaniel Clyne's cross past Tim Howard.
Southampton, with the flair and creativity of Three Lions playmaker Adam Lallana in their side, controlled the game and were good value for their first success in four outings.
Manager Mauricio Pochettino said: “"There were many positives aspects from the win today. In the overall analysis, we just followed our style.
"We played in the way we know how to play and it worked for us to play a team that is fighting to get into the Champions League as well.
"I want to thank the players, the medical staff and overall the entire club because we matched our record in the history of the Premier League."
England left-backs Leighton Baines and Luke Shaw, who made his senior debut against Denmark in March, featured on each flank, while 20-year-old Ross Barkley played in a central midfield role for Roberto Martinez's men.
Aaron Lennon and Andros Townsend both featured for Tottenham in their 1-0 win over with Stoke with left-back Danny Rose getting the winner.
Jonjo Shelvey celebrates his sensational strike for Swansea
Jonjo Shelvey, who made his only England appearance against San Marino 2012, scored a contender for goal of the season with an incredible volley against Aston Villa.
The 45-yard effort was the third goal in Swansea's 4-1 win against Paul Lambert's men at the Liberty Stadium.
The match between West Brom and West Ham was settled by a single strike by England under-21 star Saido Berahino.
On 10 minutes Stephane Sessegnon burrowed through the centre of the West Ham defence and slid a pass into the path of Morgan Amalfitano. The Frenchman sized up the situation and skidded the ball across goal for Berahino to convert.
Saido Berahino scored the game's only goal as West Brom beat West Ham
Jake Livermore and Tom Huddlestone both looked impressive for Hull in the second half after they came back from two goals down to draw 2-2 with Fulham.
Manager Steve Bruce said: “It's not often you come back from 2-0 down but if anyone will it's this lot. We showed great resilience to get something out of it.”
