Collecting the ball 40 yards out, Lingard ghosted past three Leicester defenders before calmly slotting the ball past Kasper Schmeichel.
Having scored the goal that won United the FA Cup at the same stadium 77 days earlier, it was a happy return to Wembley for the young Englishman.
Jamie Vardy equalised for the Foxes after 52 minutes, but new signing Zlatan Ibrahimovic did what he had been brought in to do and headed in the winner with seven minutes left of normal time.
Mourinho's men began their Premier League campaign with a visit to Eddie Howe's Bournemouth.
Juan Mata gave United the lead with a tap-in just a week after being substituted within 30 minutes of being brought on against Leicester, and amid rumours that he would be deemed surplus to requirements, as he had been under Mourinho at Chelsea.
The lead was doubled just before the hour mark by a Wayne Rooney header and Ibrahimovic sealed the win five minutes later with a 25-yard effort.
Adam Smith scored a consolation for the home side, but returning to Manchester with a 3-1 win - the same scoreline by which they had defeated the Cherries at the end of last season - and with world-record signing Paul Pogba still to come into the starting line-up, United fans were confident that the Mourinho era would be a marked improvement on the last three seasons.
Pogba finally made his second United debut in Mourinho's first match in charge at Old Trafford, when Southampton visited in a Friday night fixture.
Ibrahimovic dared to Zlatan twice more, continuing his stellar start to the season with another headed finish and a penalty, giving the Red Devils a comfortable 2-0 victory.
Pogba gave an encouraging first performance, while new signing Eric Bailly continued his fine start to the season (which had seen him named man of the match in both of the first two games), easing the absence of Chris Smalling by combining well with Daley Blind in the heart of defence.
If the promising start to the season looked to have banished the demons of recent times, the visit to Hull showed that there was still work to be done for Mourinho.
Against a Hull side managed by Mike Phelan and thus far undefeated despite their early-season turmoil, United enjoyed the lion's share of possession and made numerous attempts on goal, but were stymied by a lethargic tempo and an inability to trouble the scorers.
Enter Marcus Rashford. The 18-year-old entered the fray with 20 minutes left and completely changed the pace of United's play in his first appearance of the season.
Twice in the final 10 minutes, dogged Hull came close to snatching a winner, but in the second minute of added time, Rashford made the difference.
As Rooney ghosted past Mohammed Elmohamady on the left byline, he delivered a pinpoint ball across the face of the goal, with Rashford ready and waiting to tap in and bring three point back to Old Trafford.
Remarkably, Rashford's goal was the first scored by a teenager under Jose Mourinho.
Although United's attacking malaise reared its head once more, the ability to snatch victory from the jaws of a draw is a hallmark of any successful side, and it looked as if United may have rediscovered the habit.
After the international break, United took on City in the Manchester derby, and with it Pep Guardiola brought about Mourinho's first defeat of the season.
When Kevin De Bruyne and Kelechi Iheanacho gave City the lead in the first-half, there could be no qualms with City completely outplaying their rivals.
At the end of the first-half, United received a lifeline when a mistake by City 'keeper Claudio Bravo - whose signing caused the departure of Joe Hart to Torino - allowed Ibrahimovic to fire in a half-volley from the edge of the box.
United looked a much-improved side in the second half, but were unable to find an equaliser or a winner, and so City took the local spoils on this day as Mourinho realised there was still more work to be done.
As a consequence of last season's Premier League finish, United are resigned to playing on Thursday nights as part of their Europa League campaign, and last week's opener against Feyenoord certainly did not go according to plan.
With Mourinho commenting that he did not want to be in the tournament, he made eight changes from the side that played City including the absence of captain Rooney who did not even travel to the Netherlands.
With players such as Matteo Darmian, Morgan Schneiderlin and Marcus Rojo making their first starts of the season, United struggled throughout the encounter and it was not undeserving for Feyenoord when they finally broke the deadlock in the 79th minute.
United were unable to muster an equaliser, and so they fell to a fourth successive away defeat in Europe. A promising start to the season had now seen consecutive defeats. There would have to be a response at Watford the following weekend.
The visit to Watford presented United with an excellent opportunity to reverse the slide and return to winning ways. It did not happen like that.
United were supremely fortunate not to go 1-0 down when Odion Ighalo missed an open goal after David De Gea and Chris Smalling got in each other's way to deal with a long ball, but it wasn't long before Watford did break the deadlock at Vicarage Road through Etienne Capoue.
As is becoming increasingly common, it was Rashford who gave Mourinho hope by firing in from point-blank range just after the hour mark, and so United were confident of kicking on to find a winner. But best laid plans and all that...
With eight minutes of normal time remaining, Juan Zuniga gave Watford the lead within one minute of entering the fray, and Watford even found a third in the fifth minute of added time when Troy Deeney converted a penalty after Marouane Fellaini fouled Zuniga.
A 3-1 defeat was not in the script for Mourinho.
The first month and a half of the season has been a case of feast and famine. After opening up with four victories, they now face the prospect of four successive defeats if they are embarrassed by League One side Northampton Town in Wednesday's EFL Cup encounter.
Lose that and Mourinho could be in bother.
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