Shinji Kagawa broke the deadlock in stoppage time of the first half before scoring twice more after the break to complete a hat-trick.
Rooney added a fourth to complete the rout as United moved ever closer to regaining the Premier League title from rivals Manchester City.
Here, Sports Mole takes an in-depth look at yet another win for Sir Alex Ferguson's men.
On target 10
On target 1
Was the result fair?
You just have to look at the stats to see how one-sided the match was. Perhaps 4-0 was a bit harsh on Norwich as they defended very well for large periods, but there is no doubt that United deserved to win it. The Canaries didn't threaten going forward and United penned them back in their own half for much of the match.
Man Utd's performance
Dominant. As expected, they took control of the ball early on and rarely relinquished it. They struggled to create chances in the first half, but that was more down to good Norwich defending. Kagawa's second and third goals were well worked and secured a well-deserved win for the league leaders. They never looked likely to lose and did a thoroughly professional job.
Until the 45th minute, it was pretty much perfect for an away side at Old Trafford. They frustrated the hosts and limited them in terms of chances. They were the better team at the start of the second half too, but United soon regained control and Norwich were powerless to resist. Overall, they were poor going forward but strong at the back, despite the 4-0 scoreline.
Sports Mole's man of the match
Shinji Kagawa: If someone scores a hat-trick, they have to be man of the match. Each of his goals was well taken and products of well-timed runs into the box. Rooney deserves a mention for his two assists and his goal, but Kagawa looks to be finally finding his feet in the Premier League and this was his best performance in a red shirt so far.
It's not often that Robin van Persie gets this award, but his shot in the first half is the clear winner. He cut back onto his favoured left foot, but the resulting effort was closer to the roof of the stadium than the goal. A truly woeful strike.
Neil Swarbrick had a solid game. The most contentious decision he made was when Grant Holt was adjudged to have fouled Patrice Evra when going up for a header. It looked a fair challenge, but the referee disagreed and blew the whistle with Robert Snodgrass in a great position to score. The Norwich midfielder missed anyway, though, so it didn't really matter.
Man Utd: It's the big one. Next up United face Real Madrid at Old Trafford in the return leg of their Champions League last-16 tie.
Norwich: For Norwich it's slightly less glamorous home match against Southampton next Saturday.