The antipathy between Conte and Mourinho has been barely disguised, and the pair exchanged the most cursory of handshakes before kick-off.
And a measure of just how much this win meant to Conte in both a footballing and personal context could be seen in just how fired up he was throughout.
The Italian was lectured by referee Anthony Taylor for his touchline antics, was seen brandishing an imaginary yellow card, and was almost bursting out of his coat in celebration at the final whistle.
After striding on to the pitch at the full-time whistle to congratulate his players, he punched the air to all four sides of Stamford Bridge, then pumped his fist against his chest.
Conte's position at Chelsea has been the subject of much conjecture for most of this season, and he was clearly hurt by the manner of his side's Champions League defeat by Roma in midweek, but he got an instant response against United and his old adversary Mourinho.
Chelsea's win will hardly have leaders Manchester City breaking into a cold sweat, but this was a victory Conte desperately needed.
Asked about the lack of a handshake with Mourinho at the end of the game, he told Sky Sports: "It's not important. It's important to win the game.
"You have to have the respect on the pitch not outside the pitch."
Morata and Romelu Lukaku were central figures in a summer of transfer speculation as both Chelsea and United moved to strengthen their attacking resources with marquee signings.
United felt they had pulled off a coup in signing Lukaku from Everton in a £90m deal after supposedly long-standing interest from his former club Chelsea, while Conte insisted he had got the man he wanted all along when he completed a £65m move for Morata.
There was only one winner here as Morata's movement, desire and match-winning goal meant he totally outshone the Belgian.
Lukaku has not scored in his past seven games and struggled to make any sort of impact as United slumped to a disappointing defeat.
Morata, in contrast, led Chelsea's line with pace and energy and made the game's decisive contribution with a towering header after being given far too much space by the United defence.
This was another disappointing return to Stamford Bridge for Mourinho, who lost 4-0 against his former club in the Premier League last season and was also on the wrong end of a 1-0 defeat in an FA Cup quarter-final.
And, while it would be harsh to accuse Mourinho of parking the bus, it was yet another cautious performance from United until they went behind to that magnificent header from Morata.
Mourinho will have every right to question how Morata could find so much space around Eric Bailly, Chris Smalling and Phil Jones - but ultimately United left their push too late.
Fellaini was thrown on to add his usual mix of physicality and nuisance value, almost scoring with a scrambled shot that Courtois pushed away, while Rashford was narrowly off target with a snapshot and a free-kick.
But, yet again, there remains the lingering feeling United could have secured a more satisfactory result by adopting a bolder strategy - and this loss means Manchester City are now threatening to disappear into the distance.
Chelsea manager Antonio Conte on Sky Sports: "It's an important victory. When you play against Manchester United it's always a massive game. We know very well this team is very strong. This type of win is important for our confidence. We showed great desire and passion to win this kind of game.
"We can win or lose but our spirit must be this. Last season our spirit was in every game - we started this season with a lot of problems. We were up and down. This game showed if we want, we can."
Manchester United boss Jose Mourinho: "It was an even match. Both teams could win. The first to score would be in more defensive control and to win the match.
"The first half was really even. In the second half in the only period where they were on top of the game, they scored.
"It frustrates us to concede a goal in this situation. We lost ourselves after the goal emotionally. We found again the balance and desire in the last 15 to 20 minutes. It was all us.
Alvaro Morata scored the only goal of the game as Chelsea beat Manchester United 1-0 at Stamford Bridge on Sunday.
The former Real Madrid striker broke the deadlock for the south-west London club with a spectacular header ten minutes after the break.
The goal was Morata's first in seven games, and was enough to secure all three points for Antonio Conte's men, who remain fourth in the table.
Cesar Azpilicueta claimed the assist after firing the ball into the box and finding his fellow countryman, who leaped higher than his marker.
