Kagawa's first goals since the defeat to Tottenham in September illuminated proceedings at Old Trafford and Wayne Rooney added a sensational fourth in the final minute with a long-range special.
After scoring in first-half injury time, the Japan schemer produced two of the calmest finishes you are ever likely to see before Rooney wrapped up a convincing win against the Canaries, who inflicted the Reds' last defeat at league level in November.
With Manchester City not in action until Monday, the Reds can enjoy a sizeable lead at the summit whilst beginning to prepare for the visit of Real Madrid.
Sir Alex Ferguson fielded a strong side despite the European tie with Real looming large on Tuesday but a slow-paced start offered some encouragement to the visitors and Bradley Johnson made a hash of his cross after finding a lot of space out wide.
Although Javier Garrido hacked away when Nemanja Vidic met a Robin van Persie free-kick with a header, the first real sight of goal came after 15 minutes when a slick move saw Rooney attempt to find van Persie but Mark Bunn was out to save bravely at the Dutchman's feet.
The first shot on target was a tame one, 10 minutes later, with Michael Carrick's harmless daisy-cutter rolling through to Bunn, and it was only around the half-hour mark that the Reds started to click into gear. To their