In the process, the Red Devils not only extended their lead at the top of the table, but also warmed up for their Champions League duel with Real Madrid in fine style.
Although Sir Alex Ferguson had promised his team would be fully focused on the "mundane" domestic fare immediately prior to the most glamorous of European nights, for most of Saturday afternoon's contest they were well below par.
It seemed even the home fans spent much of the afternoon wondering what lay ahead rather than bother about what was in front of them.
Eventually though, United cut loose, netting three times in the final 14 minutes, with Kagawa grabbing two to complete a memorable three-timer before Wayne Rooney belted in a sensational effort as United's grip on the title tightened.
Given Ferguson's liking for fooling around with the media, it was no surprise that, after all the eulogies ahead of what would have been the 1,000th senior appearance of Ryan Giggs' career, the veteran Welshman duties were no more arduous than climbing the steps of the directors' box to watch.
Rafael and Rio Ferdinand were other notable absentees ahead of Tuesday's meeting with Real Madrid, deemed so important by Jose Mourinho that he could do without Cristiano Ronaldo for the latest 'El Clasico' with Barcelona.
At a rough guess, either six or seven of United's starting line-up will keep their places next week, and they are bound to do better than the low-key offering served up during a dreadful first-half that only livened up in stoppage time.
Up to that point, a brave Mark Bunn dive at Robin van Persie's feet and a low Michael Carrick effort that barely troubled the Norwich keeper were United's only threat.
Van Persie's form has dipped in recent weeks and a shot the Dutchman ballooned into the Stretford End midway through the half summed up the entire affair.
With Norwich's defence marshalled superbly by Bradley Johnson and Robert Snodgrass flying into challengers to expose any trepidation in United ranks, the visitors could feel well pleased with their efforts.
Their good work was undone in those additional couple of minutes though.
Antonio Valencia stepped neatly inside Anthony Pilkington on the edge of the area before floating over a rare left-footed cross.
It was not exactly perfect for Van Persie. But when he stretched to control, the ball bounced down for Kagawa, whose shot caught Bunn by surprise as it crept in at the near post.
For Kagawa, it was a welcome moment.
A debut season halted by a knee injury in October has not really caught fire again.
And despite Saturday's heroics, he looks set to be one of the players to lose their place from the team that performed so well in the Bernabeu.
Patrice Evra is one of the certainties to be retained. Little wonder therefore that Ferguson was so annoyed when Snodgrass launched into the French full-back in the dregs of the half.
Evra was none too pleased either, although he did return for the second-half and Snodgrass collected a yellow card.
A sliced clearance over his own bar from Nemanja Vidic straight after the re-start was an indicator not much had changed from the unconvincing first-half display.
Jonny Howson had an effort deflected wide before Grant Holt got above Evra and steered a cushioned header into Russell Martin's path, only for the full-back to lift his effort over from barely four yards.
That Holt was fouling Evra was not really the point, just the finishing which was so obviously lacking finesse.
And though United continued to coast in second gear, and though Van Persie was replaced by Danny Welbeck, they were still too good.
Indeed, barely any pressure had been applied to the visitors' box when Rooney sped into the box 14 minutes from time and supplied the pass from which Kagawa doubled his tally for the season.
Kagawa was not finished though and another Rooney assist created a further opening for the Japan star, who again finished clinically to complete his hat-trick.
Rooney has a few of those of course.
On this occasion, his goalscoring intervention was more brutal as he lashed a ferocious effort past Bunn in the final minute.