Even with Jose Mourinho watching on, Real Madrid seemed to be the last thing on United's minds as Ryan Giggs and Robin van Persie scored the first-half goals that were enough to see off a dogged Everton, keeping the Reds well clear atop the table after Manchester City's shock defeat to Southampton on Saturday.
Giggs has now scored in a remarkable 23 successive league seasons, yet another milestone in an unparalleled career, while for Van Persie, it was the 23rd goal of a sensational debut campaign.
United almost made the perfect start as Wayne Rooney threaded a pass through to Van Persie, which allowed the Dutchman to cruise round Tim Howard, but he surprisingly turned his shot on to the post.
But it was not long before Giggs' shot was rolling in off a post after Van Persie had set him up. It extended the veteran Welshman's remarkable record of scoring in all 21 Premier League seasons and means he has now found the target in 23 campaigns.
Much like the corresponding fixture last season, when they twice came back from two goals down to clinch the draw, Everton responded with vigour. David de Gea produced an excellent flying stop to deny Leon Osman and Kevin Mirallas' cross was not quite accurate enough for Victor Anichebe, who would have had the goal at his mercy.
United defender Nemanja Vidic threw himself into the fray, literally at times, with relish, while danger-man Marouane Fellaini picked up a shadow in Phil Jones, who nullified the Belgian's threat. However, Jones took a knock in the first half and headed straight to the dressing room for treatment after failing to run it off in the second.
The hosts defensive efforts kept Everton at bay, and when Rafael supplied Van Persie with a similar chance to the one he had spurned earlier, this time the Dutchman's finish, after again rounding Howard, had greater accuracy and just too much power to prevent Johnny Heitinga from keeping it out.
United managed to keep Everton at arm's length for most of the second period. They might well have increased their lead too, only for Jonny Evans to be left bewildered at how he was denied three times within the space of five seconds.
Two Tim Howard saves and a scrambled Nikica Jelavic clearance frustrated the Northern Irishman. Meanwhile, Rooney's last-minute header to deny Heitinga a shooting chance epitomised the effort United had put in at the back, with De Gea also saving from Jelavic late on.