The Belgium international provoked the wrath of the Toffees faithful after celebrating when he netted a close-range finish to put United 3-0 up.
A further strike from Anthony Martial from the penalty spot set an emphatic final scoreline of 4-0 in Jose Mourinho's men's favour.
Lukaku has settled perfectly into life at Old Trafford, and his latest goal took him level with two former United favourites who also made brilliant starts at the club.
Only Saha and Van Persie had previously netted five goals their first five Premier League games for Manchester United, and now Lukaku joins that privileged club.
United will be hoping that the goals keep flowing, as they sit pretty at the summit level on points with bitter rivals Manchester City at this early stage in the season.