United had looked on course for a comeback win but hat-trick hero Cole Palmer scored the latest-ever winning goal in a Premier League game - after 11 minutes of added time - having equalised only a minute earlier from the penalty spot.
"I've had every emotion today. At times I've been on the floor but at times I was high as a kite," former United defender Rio Ferdinand said on TNT.
"Cole Palmer was the shining light throughout the game. You have to pay respect to him, he's the jewel in the crown now. This is what the Premier League is about, the Chelsea fans were leaving but came back in when that third goal went in."
Ex-Brighton & Hove Albion striker Glenn Murray was also dazzled by Palmer's performance, telling the BBC: "We said it was season-defining and a hat-trick for Cole Palmer, boy can they build a team around him.
"We have just seen something very special here at Stamford Bridge."
Former England and Chelsea player Joe Cole said the match would go down as one of the best ever been played at Stamford Bridge.
"I'm delighted, I love football, I love moments like this," Cole said on TNT.
"All of these people watching come here and watch their team never give up and give them a moment. This will go down as one of the great games in this stadium, mark my words.
"For this team, this could be so important. It's all about the moment, no other sport does this. It's amazing."
With the teams combining for a total of 47 shots, defenders were under fire and on the back foot.
Former Chelsea player Craig Burley blasted both teams for their porous defences, saying on ESPN: "That's what happens when you have two big clubs who have spent a fortune and are still a shambles.
"That's what you get, a chaotic match that neither can control from start to finish.
"It was the 'Battle of the Shambles'. It looked like Chelsea would come out looking slightly less shambolic, which they did at the end."
