Substitute Ross Barkley struck with virtually the last kick of the game in the 96th minute to salvage the hosts' unbeaten start under Maurizio Sarri and spark a touchline melee as Mourinho took offence at the excessive celebrations of one of Sarri ' s backroom staff.
However, there were also positives for Mourinho as the visitors showed plenty of heart and no little skill to fight back from a goal down thanks to Anthony Martial ' s double .
AFP Sports looks at three things we learned :
Martial firing
Mourinho' s struggles at Old Trafford are encapsulated in his troubled relationship with Martial, with the Frenchman failing to deliver on his rich potential over the past three seasons.
However, the 22- year -old cannot be accused of failing to play for his manager in his time of need.
Martial' s composed equaliser transformed a game in which United had been outplayed for the first 55 minutes .
His second was an even sweeter finish that showed what United are capable of with Juan Mata and Marcus Rashford also playing their part in a flowing move .
" Martial is improving, he is doing different things than before, " said Mourinho . " He is a more complete player than before but he needs to improve. He has a huge talent and he wants it , which is a good thing. "
Hazard warning for Chelsea
Sarri complained that Chelsea stopped playing " his football " after Martial levelled , and were too easily panicked into playing long balls.
Alvaro Morata again failed to act as a reliable focal point and his replacement Olivier Giroud is still without a goal this season.
The lack of an in- form striker has so far been papered over by the stunning form of Eden Hazard .
But the Belgian was blunted by some rough treatment by United early on as both Nemanja Matic and Ashley Young were booked .
On this evidence , Hazard can expect more bruises in the coming weeks as it becomes clear that if you stop him , the rest of the Chelsea attack is pretty blunt.
Pogba zones out
Unlike against Brighton , Tottenham and West Ham this season, United did not lose , but in common with those games they did once again concede from a corner .
Paul Pogba was at fault as Antonio Rudiger was given a free run to power a header past David de Gea and give Chelsea the perfect start .
Mourinho refused to criticise Pogba individually but for a coach whose success has been built on defensive solidity , patience with such a basic weakness is wearing thin .
" My feelings is that we work . We work on the pitch, the analysis, the preparation, " said Mourinho.
" We defend mixed, so some of the players are in zone , some have individual opponents . Every player knows the zone or the man, but sometimes the opponent is better than us . "
( AFP)