Dominant in the opening half hour, all Conte’s Chelsea had to show for that period was a superb breakaway goal from Willian.
And when United finally came to terms with the challenge posed by Willian and Eden Hazard, and Mourinho’s tactical masterplan, a goal and assist from Romelu Lukaku condemned Chelsea to their seventh league defeat of a miserable title defence.
“Of course we are disappointed,” said Conte. “For sure we must be disappointed after the start we had, a team today who had every chance to get three points towards a place in the Champions League.
“But again we are talking about another defeat and we must be disappointed because when you have this type of situation you have to manage the game better and you must be able with experience and maturity to get three points.
“But instead another time we are talking about a loss and you must be very disappointed with this.”
Certainly, on current form, Chelsea would seem odds-on favourite to lose out to Liverpool, Tottenham, and United in that contest for the three coveted Champions League positions behind champions-elect Manchester City.
Conte’s complaints about a team lacking experience and maturity in such situations seemed a little disingenuous, considering it is only nine months since they were being crowned champions in the Italian’s first season.
“This could be our position for sure, to miss out,” he said. “I’m repeating the same thing many many times — in this league to find a place in the Champions League is not simple.
“It is not easy because in this country it is the only championship where you can find six teams at the start to fight for four places.”
Yet, for 30-something minutes at least, Chelsea were purring, Willian and Hazard pulling the strings of a sublime display that could have seen the visitors in front after just four minutes from a move that Mourinho admitted left even him lost for words.
Antonio Rudiger found Hazard whose pass wide was met by Marcos Alonso with a ferocious first-time volleyed cross which Alvaro Morata, in turn, volleyed against the bar. Hazard might even have netted the rebound only for David De Gea to tip over.
Despite Hazard and Willian dominating the opening half hour, it took until the 32nd minute for Chelsea to make the pressure tell.
Willian and Victor Moses broke up a United attack in their own area before the Brazilian sped upfield, passing to Hazard and continuing his run past bemused United defenders and receiving a return pass.
He eventually unleashed a fierce shot from eight yards which De Gea should probably have saved — the start of an uncomfortable afternoon for the Spanish international who would go on to fumble a Danny Drinkwater free-kick and almost allow a Willian free-kick to go in at his near-post.
By then, however, United had finally started to find their own rhythm, winning the ball more frequently in midfield and starting to stifle the playmaking Chelsea pair.
After 39 minutes, Lukaku battled for the ball, eventually tussling with Andreas Christensen on the edge of the Chelsea area before neat passing from Nemanja Matic and Alexis Sanchez played him clear on goal.
There was still work for Lukaku to do but he did it, holding off Alonso impressively and finishing emphatically from eight yards.
Arguably, his role in United’s 76th-minute winner was even more impressive as he gathered a crossfield pass from Scott McTominay and spotted the darting run of substitute Jesse Lingard.
His perfectly weighted centre hung in the air long enough for Lingard to capitalise on some slack defending by Chelsea’s back three, by Christensen in particular, and head past a stranded Thibaut Courtois.
“He played fantastically well,” said Mourinho. “He had, in my opinion, the same start as the team; the team didn’t start well, the team didn’t start very confident and it happened to him.
“He was a little bit lost but then he went together with the team, the team was improving, improving, improving.”
As were United and Lukaku might have scored a winner himself, before assisting on it, with a spectacular volley which Courtois saved brilliantly.
In the end, however, after Morato had a late ‘goal’ harshly ruled out for offside, the abiding image of the day was of man of the match Lukaku booting the ball long upfield then chasing after his own ‘through ball’, outpacing three defenders before seeing his own shot blocked by Christensen.
A few seconds later, the final whistle blew and Mourinho and Conte shook hands for a second time, to end their dispute.
“The handshake doesn’t need any words,” said Mourinho. “I think that’s what me and Antonio want to show to everyone.
“And the handshake before and after the match is an example that everything in football you have to move and you have to respect each other.
“Mourinho and Conte are not two ordinary people in football, we have a history and an image and we have to be happy with that.”
De Gea 5; Valencia 6, Lindelof 7, Smalling 6, Young 6; McTominay 7, Matic 7, Pogba 6; Sanchez 6, Lukakau 9 (Bailly 80), Martial 5 (Lingard 64, 7).
Mata, Carrick, Rashford, Shaw, Pereira.
Courtois 7; Azpilicueta 7, Christensen 5, Rudiger 6; Moses 7 (Giroud 77, 5), Kante 7, Drinkwater 5 (Fabregas 80), Alonso 7; Willian 8, Morata 6, Hazard 7 (Pedro 72, 6).
Caballero, Fabregas, Pedro, Giroud, Zappacosta, Cahill, Palmieri.
M Atkinson 7