At the other end David De Gea was forced into fine diving saves from David Luiz and N'Golo Kante but was powerless as Barkley hammered home after Luiz's header hit the post in the sixth minute of injury time.
United looked sure to claim all three points until the late drama; first Luiz hit the post with a header, Rudiger's follow up was superbly saved by De Gea, before Barkley drove into the goal easily.
The 35-year-old was injured in an aerial challenge in the ninth minute and appeared to swallow his tongue as he landed, before being taken off on a stretcher after six minutes of treatment on the pitch.
He said: "Oh come on, I can tell you that 97 minutes of the game was so good that you have to focus on that".
"I'm not annoyed with anything".
The charmless episode left Sarri accepting that the Chelsea bench was in the wrong and ordering his assistant to apologise to Mourinho.
"In different moments, the moments where he was not selected or not playing regularly, he was saying the same all the time: "I want to play for you, I want to play for United, I'll make it and I'll be the player you want me to be". "(Mourinho) is a very good manager and one of the best in the world.
"I did not get respect back from Chelsea [fans] but that is not my responsibility". Mourinho, who accused Chelsea's fans of disrespecting him, also attempted to draw a line under the matter despite saying that Ianni's actions were down to a "bad education". Apart from that, it's just another match for me.
"I think I would always think where I am, which stadium I'm in and which public is in the stands". But I have that situation immediately. "I will speak to him again tomorrow".
"I would love to have him in Manchester United but I don't think Chelsea will sell him to Manchester United", said the United boss.
After initially being held back from chasing the Chelsea staffer down the tunnel, Mourinho sat calmly back down on his seat - no doubt still fuming inside.
Sanchez capped the dramatic comeback against Newcastle with a stoppage-time victor and Mourinho has insisted he wants his team to always play with as much attacking intent as they did in the second half against Rafael Benitez's side.
Whether Mourinho can restore his grip on Manchester United will hinge in large part on the outcome of a daunting run of fixtures over the next few weeks.
United were on the verge of securing their first win at Stamford Bridge since 2012 after mounting an impressive comeback in the second half, with Anthony Martial scoring twice after Antonio Rüdiger had given Chelsea an early lead.