Wayne Rooney's return to his former club was the headline in the buildup to the match, but Antonio Valencia soon stole the spotlight with a stunning strike to give United the lead after just four minutes.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute coverage below.
It will be all eyes on Wayne Rooney today as he returns to the 'Theatre of Dreams' for the first time since his summer exit, but the two clubs themselves have plenty to focus on following vastly differing starts to the season. United have begun the campaign very strongly, whereas Everton have failed to live up to expectation thus far, so the pressure is on the visitors to respond here.
Before we take a closer look at that, though, let's first check out the team news...
Well, the headline news as far as the home side are concerned is that Marouane Fellaini comes in against his former club, replacing the injured Paul Pogba as expected. Fellaini, who scored 33 goals in 177 appearances during his time with the Toffees, has been lavished with praise by Mourinho in recent weeks and is subsequently handed a start this afternoon, with Herrera forced to settle for a place on the bench.
Fellaini scored when replacing Pogba during the midweek win over Basel and will be a threat from set pieces again against his former club today.
Lukaku has scored four goals in his first four Premier League games for Manchester United, and another one today would see him become only the third player to make it five in five - after Louis Saha and Robin van Persie. Across all competitions, Lukaku already has six goals in as many games for United.
Should the Belgian score today then he would become the fourth-youngest striker to reach 90 Premier League goals, after only Michael Owen, Robbie Fowler and a certain Michael Owen.
Elsewhere, Mkhitaryan retains his spot having registered a league-high five assists already this season.
You'd expect the former England captain to be given a hero's welcome following a hugely successful 13-year stay at United, during which time he won every trophy available to him and scored a club-record 253 goals in 559 appearances.
Rooney has two goals in nine appearances for Everton since his move, but both of those goals have come in four Premier League outings.
However, Rooney lost all four of his games against United during his first stint at Everton and failed to score against them during that time too.
Sigurdsson has been directly involved in six goals in his last six Premier League appearances against Man Utd (three goals, three assists), including netting in his last appearance at Old Trafford in April for Swansea.
He starts just behind Rooney up front today in his favoured number 10 position, with Sandro Ramirez on the bench.
There is likely to be a change in formation too, with Everton reverting to three centre-backs as Williams joins Keane - another former United player - and Jagielka in defence. Martina and Baines will provide the width as wing-backs.
Mourinho, by his own admission, did not bring in as many new faces as he would have liked, but Lukaku in particular has made a significant difference already and United as emerged as one of the favourites for the Premier League title at this early stage of the season having dropped just two points so far.
United's only dropped points so far this season came against Stoke City in their most recent Premier League outing, while they have also conceded a league-low two goals so far.
Couple that with a clean sheet in each of their victories so far this season and you have a recipe for success which is serving Mourinho's side well in the early stages of the season.
Ten points from their opening four Premier League games represents their best start to a season since the days of Sir Alex Ferguson too, so the signs seem to be pointing towards United heading in the right direction.
There is still a long, long way to go, of course, and it should be noted that United have not exactly had the most difficult start to the season, but having seen their dominance over English football end almost as soon as Ferguson's reign also ended, it will feel good for the club to be back at the top of the pile again.
Including their final home game of last season United have now won their last four games at Old Trafford without conceding a goal, and you have to go back more than a decade to April 2006 for the last time they strung together five wins and five clean sheets on the bounce in front of their own fans.
Manchester City were the last visiting side to taste victory here all the way back in September 2016, since when United have won 21 and drawn 11 of their 32 outings on home soil across all competitions.
However, despite ending the transfer window as one of the biggest spenders in the Premier League, Everton have made a poor start to their campaign and already find themselves playing catch-up in the race for a top-six spot.
Even more worryingly for Ronald Koeman's side are their struggles in front of goal since Lukaku's departure; Everton have scored just twice this season, with only goalless Crystal Palace managing fewer than that in the Premier League so far.
The Toffees did manage a draw with Manchester City - the only team to take points off them this season - and were only denied the victory by a late equaliser in that match, but they have subsequently been comfortably beaten by Chelsea and Tottenham.
Things got no better in midweek, though, as Everton put in a truly dreadful display against Atalanta in the Europa League, falling 3-0 down before half time. The Italian hosts could not add to their lead in the second half, but the Everton performance was not much better and they never really looked like getting back into the game.
Today's match is a very difficult one to have follow such a lacklustre display, but Koeman will be demanding a reaction from his side nonetheless.
The Toffees' poor form includes an ongoing three-match losing streak, during which time they have failed to even score a goal, and you have to go back to January 2015 for the last time they lost four games on the bounce and April 2006 for the last time they failed to score in four consecutive matches.
That run includes an ongoing 10-match winless streak which has seen them pick up just five points from the last 30 available on the road, and should they fail to win today then it would be their worst away run in the league for 13 years.
These two sides come into this match in such contrasting form that it is difficult to see anything other than a home win. Koeman will be demanding a response from his side following their dreadful showing in midweek, but whether they will be able to muster a good enough one against a United side in fine form is a big ask for the visitors. Add to that their poor away form and United's perfect start at home, and we have to go for a home victory.
Sports Mole says: Manchester United 2-0 Everton
That solitary victory came during David Moyes's time in charge of United when Bryan Oviedo scored the only goal in a 1-0 victory in December 2013.
Should United win again today then they would equal the Premier League record for most wins against a single opponent, equalling their tally of 34 against Aston Villa.
The most recent meeting in April also came at Old Trafford, and Everton were a whisker away from slightly improving their record at the ground after Phil Jagielka's goal had given them the lead. However, Zlatan Ibrahimovic rescued a draw with a penalty deep into stoppage time as United denied Koeman's side at the death.
MAN UTD STARTING XI: De Gea; Valencia, Bailly, Jones, Young; Matic, Fellaini, Mata, Mkhitaryan, Rashford; Lukaku
EVERTON STARTING XI: Pickford; Martina, Keane, Williams, Jagielka, Baines; Schneiderlin, Gueye, Davies; Sigurdsson; Rooney
Manchester United make a perfect start to the match as Antonio Valencia hits an absolute worldie in from the edge of the box! The full-back is left unmarked on the edge as the ball is played across from the left side of the pitch by Matic, and Valencia opts to take it on first time. He couldn't hit it any better and, while it isn't right into the top corner, the power on it leaves Pickford no chance.
An early contender for goal of the season!
7 - Manchester United have now had more different goalscorers in the Premier League than any other team this season (7). Spread.— OptaJoe (@OptaJoe) September 17, 2017
The Belgian does the hard part by beating a scrambling Williams in the area, but with only Pickford to beat he places his finish wide of the target when he really should have scored! Old Trafford was just waiting for the net to bulge then!
Martina's initial delivery into the box is a peach which finds Davies, but his diving header from the offside position is well saved by De Gea. Sigurdsson subsequently tucks the rebound home, but the referee's whistle has already gone.
It looked like it might be worse for the Toffees considering the start they made to the game, but they settled into the match and - while United have still been the better team - Everton remain very much in this game.
Martina's cross was flicked into the path of the Iceland midfielder, who misses the ball with his first attempt but then beats teammate Rooney to the ball with his second bite at the cherry. De Gea is quickly off his line to close down the angle and make the save, though, and another good opportunity goes begging for the visitors.
The Everton defender sees his pass out from the back blocked by Fellaini, which immediately sets Lukaku off in a dangerous position. The striker is unselfish and draws the defenders before playing the ball through to Mkhitaryan, who applies the finishing touch past Pickford.
Nevertheless, it is a fourth consecutive defeat without scoring for the Toffees, whereas United move back level with Man City at the top of the table.