Antonio Rudiger's header gave the hosts the lead in the first half but Anthony Martial got Jose Mourinho's side in the driving seat with a pair of strikes.
But second-half substitute Ross Barkley pounced on a rebound in closing stages of the encounter to salvage a point for the Blues that ensured their unbeaten run in the English top-flight continue.
The atmosphere was marred by actions on the touchline when coach Marco Ianni celebrated Barkley's equaliser in front of Mourinho.
And Nigerians have had their say on the result of the game and the conduct of one of Chelsea's assistant managers.
Jose Mourinho 🙌🙌🙌 #CHEMUN— Areo Samueli O. (@Undisputed_Jsam) October 20, 2018
Mourinho telling Chelsea Fans He won 3 EPL for them is just like reminding your Ex you were the one that deflowered her so that she can be humble to you😁😁😁— Genius Joker NG 🇳🇬 (@GeniusJokerNG) October 20, 2018
Jose Mourinho might not be leading Manchester United the way many would like but he sure knows how to get a result when he's up against his nemesis. You just can't beat him time and time again without him reacting back. #CHEMUN— Olakunle FAYIGA (@k_ef4real) October 20, 2018
#CHEMUN— Frank Edoho (@frankedoho) October 20, 2018
Don't start Morata.
Start Pedro. Jorginho needs to be alert at all times. Hazard was poor today. David Luiz' erstwhile good game marred by Mata dummying him into another dimension. Chelsea class by applauding Mata at one goal down. N'golo Kante is priceless. Great game!
Disgraceful from Chelsea. Mourinho has tried to be calm all afternoon. But he still gets attacked by a Chelsea staff. No class. See why Mourinho is who he is? You’re the problem, not Mourinho. #CHEMUN #PL— Bolarinwa Olajide (@iambolar) October 20, 2018
But why are the Chelsea fans celebrating like it's a win??🤷🏽♂️🤷🏽♂️🤷🏽♂️— A.Y (@Diarogba_J) October 20, 2018
it would have a noisy atmosphere after now. The 2-2 draw was a fair result to both teams. Chelsea weren't at their best today.— Olatunde Liadi (@OlatundeLiadi) October 20, 2018
What a game! WHAT A GAME! #CFC— Babs 🦅 (@BabatundeCASH) October 20, 2018
Mou wants respect? The same man who called Wenger names?— Editi Effiòng (@EditiEffiong) October 20, 2018
Most of my fellow Chelsea fans won't admit it, but Manchester United should be admired for coming to Stamford Bridge and turning around their fortunes after going a goal down and almost winning the game. Good game. #CHEMUN— Frank Edoho (@frankedoho) October 20, 2018
It would be so annoying to see people talk more about what happened on the touch line than Manchester United's good second half.— Biola Omowanle (@Beeorlicious) October 20, 2018
Na that goal pain Mourinhoe no be the celebration— EMIR (@Jydeskillz) October 20, 2018
Yes Jose Mourinho has done that more than once. He once ran across the field against Barcelona. At Anfield, when Stevie G slipped, he kept pounding his chest at Kop. But today, that Chelsea staff was wrong. Go and boil stone if you disagree!— Bello El-Rufai (@B_ELRUFAI) October 20, 2018