Gylfi Sigurdsson's late penalty ensured an anxious end to proceedings for the hosts but, with United's legendary former star Eric Cantona watching from the stands, his fellow countrymen did enough to secure three points.
Lukaku has not scored for his club since September 15 and manager Jose Mourinho has taken the decision to leave him out of the team to face his former club.
"The thing I like is the desire to take it", said Mourinho. "I am in good form in this moment, so I have to train hard and continue to help the team". "It was hard for us. I feel that he has the same kind of feelings towards me".
"The penalty had a big impact in the match and we did not deserve this result", said Marco Silva.
And in an unfortunate, but timely moment during United's pre-match warm up, Lukaku first touch in the session was far from great. "The important thing is it went in and I scored the goal - good for us and me". I've been a player and if I'm in that game, on the pitch and as close to incidents like that as you can get, it's not a penalty.
With options a-plenty to choose from, our Portuguese supremo selected the same starting line-up that began against last week against Crystal Palace: Pickford, Digne, Zouma, Keane, Coleman (c), Gana Gueye, Gomes, Sigurdsson, Walcott, Bernard and Richarlison.
Everton were livid that Idrissa Gueye was judged to have tripped Martial as he darted into the area after 27 minutes although, in truth, they could consider themselves fortunate that then midfielder was not sent off, having picked up a yellow card five minutes earlier. "I came up for the corner but it wasn't to be".
Matic also stressed the need for United's attacking players to show more of a ruthless edge in front of goal as Mourinho's men scuppered a handful of chances to put the game to bed before Everton pegged them back. There was certainly minor contact, but the plunge by Martial was uncalled for and even Graeme Souness and Jamie Redknapp felt it was a harsh call.
The England goalkeeper saved from Pogba after the Frenchman gave a stuttering run-up to his 27th-minute spot-kick, but was unable to keep out the rebound as United opened the scoring.
"This victory was very important to get us back toward the top of the league".