Although manager 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 this afternoon's contest they were well below par.
Eventually, though, United cut loose, netting three times in the final 14 minutes, with Kagawa grabbing two of those to complete a memorable treble 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 was not even in his matchday squad.
Defenders Rafael and Rio Ferdinand were other notable absentees ahead of Tuesday's second-leg meeting with Real Madrid, deemed so important by Jose Mourinho after a 1-1 draw in the Bernabeu last month that he could do without Cristiano Ronaldo for today's league match with Barcelona.
United took the lead in the dying moments of the first half when Kagawa's shot caught goalkeeper Mark Bunn by surprise as it crept in at his near post.
A second was added when Rooney sped into the box 14 minutes from time and supplied the pass from which Kagawa doubled his tally.
The same pair linked up for Kagawa to again clinically finish and complete his hat-trick, before Rooney lashed a ferocious effort past Bunn in the final minute.