Mourinho’s side were holding onto a slender lead given to them by Anthony Martial when Lingard took possession with nine minutes left at Goodison Park.
Seconds later the points were in the bag as the 25-year-old weaved through the Everton defence and curled a fine finish into the top corner.
It was Lingard’s 10th goal of the season and his fourth in his last five appearances.
After spending much of his United career struggling to hold down a place, Lingard has thrived under Mourinho, who was full of praise for his development.
“One thing is to be a young talent, another thing is to be a very good player,” Mourinho said.
“Some players are not capable of that jump. They go from great potential to normal players. Lingard is giving that jump.
“He is more consistent, he is adaptable, he understands better the game, he is going in a good direction.”
Lingard’s contribution wrapped up United’s first win in four games after a run of draws had left them lagging behind Premier League leaders Manchester City.
United are still 12 points adrift of their Manchester rivals, but Mourinho, who has criticised his stars recently, took heart from the way his players battled to subdue Everton.
“Our pride, our effort, everything was top class and on top of it we played very well,” he said.
“It wasn’t a performance of tired boys, with the worst possible calendar that you gave us.”
Mourinho has called for substantial backing from United’s owners as he plots several signings in a bid to catch City.
Asked if he would be bringing in new faces in the January transfer window, Mourinho added: “I don’t know about transfers.
“In this moment we are in trouble, in two to three weeks time maybe we recover and we breathe in a different way.
“Can we improve now or do we wait util the summer? I cannot say.”
After a dull first half at Goodison Park, Jose Mourinho‘s side upped the tempo after the break and were rewarded as Martial struck from distance just before the hour.
Everton tried to respond but Lingard ended their hopes as he doubled United’s lead, and lifted them back to second in the Premier League, with a superb individual effort.
TWEET OF THE MATCH
Cracking goal. As it’s now a thing, it’s worth pointing out that Martial has scored more goals in this calendar year than Messi, Ronaldo, Kane and Neymar combined.
— Gary Lineker (@GaryLineker) January 1, 2018
STAR MAN – PAUL POGBA
Pogba and Juan Mata took charge of the game in the second half, driving the pedestrian United forward at every opportunity.
Mata’s trickery and vision troubled Everton while Pogba’s passing and forceful runs constantly pushed them back.
Both also went close to scoring but Pogba probably just shaded it as to who was the most influential.
MOMENT OF THE MATCH
The first half was dreary but United woke up after the restart.
Mata twice went close with spectacular efforts and Martial changed the complexion of the game with a fine finish but Lingard’s goal was the most eye-catching moment.
His strike was a brilliant solo effort from the edge of the area after a penetrative run.
IN THE CROWD
Wayne Rooney had a disappointing afternoon as he came up against his former club.
He is clearly still remembered with some fondness by United fans – and rightly so – given he is their record goalscorer as they chanted his name early in the game.
They soon made clear he is no longer their favourite, however, with the next chant implying he is overweight.
Jordan Pickford 5
Mason Holgate 6
Michael Keane 6
Ashley Williams 6
Cuco Martina 6
Tom Davies 5
Morgan Schneiderlin 5
Nikola Vlasic 6
Wayne Rooney 5
Yannick Bolasie 6
Oumar Niasse 5
Aaron Lennon (for Bolasie, 62) 5
James McCarthy (for Rooney, 62) 6
Dominic Calvert-Lewin (for Niasse, 81) 5
David de Gea 5
Victor Lindelof 5
Phil Jones 6
Marcos Rojo 6
Luke Shaw 6
Paul Pogba 7
Nemanja Matic 6
Jesse Lingard 6
Juan Mata 7
Ander Herrera 5
Anthony Martial 6
Marcus Rashford (for Martial, 77) 5
Daley Blind (for Lingard, 87) 5
Axel Tuanzebe (for Mata, 90) 5
Rooney, now Toffees captain, rejoined his boyhood club last summer.
Here, Press Association Sport looks at how Rooney performed.
Playing in a deep role, Rooney was not really a threat in front of goal. He did try his luck with a long-range shot in the fourth minute but that was deflected for a corner. Beyond that, Rooney did not look like scoring.
Some of Rooney’s most notable runs were made for defensive reasons.
Never shy to get stuck in, the Everton skipper often back-tracked to try to break up Everton attacks.
He did so very effectively once in the first half as United probed outside the area, but other efforts were not successful.
He was booked for a poor challenge on Anthony Martial and later gave the ball away prior to the visitors taking the lead.
Rooney took responsibility for most of Everton’s set-pieces but had no joy.
An early cross into the box from a free-kick was particularly wasteful while his corners, mostly taken from in front of the United fans, were easily dealt with.
In terms of vision and awareness, Rooney could not be faulted. He spotted runs of team-mates and looked to pick them out while also creating gaps.
Unfortunately for him, the execution was not there and many of his passes were misplaced.
Rooney was his usual hard-working self but this was not one of his better outings.
United handled their former star player comfortably and he could not stretch them.
One of his errors led to a United goal and, with the visitors getting on top in midfield, it was understandable that manager Sam Allardyce withdrew him just after the hour.