Diego Costa scored a late equaliser to preserve Chelsea’s unbeaten record under interim boss Guus Hiddink and deny Manchester United a win.
United dominated early on, Thibaut Courtois producing a fine one-handed save to keep out Anthony Martial.
David de Gea saved well from Nemanja Matic’s header before Jesse Lingard’s fine turn and shot put United ahead.
Costa rescued a point in the 91st minute after rounding De Gea following Cesc Fabregas’ pass.
United were moments away from moving to within four points of the top four when Costa scored his seventh goal in eight games.
Chelsea, who lost defender Kurt Zouma to a serious injury, remain 13th in the table.
Chelsea manager Guus Hiddink:
“I am happy with the reaction of the team. Manchester United did a good job in the first half and in the beginning of the second, they are not an easy team to beat.
“But we deserved a point. We dropped too far back after the first 20 minutes when they dominated us but later on we closed a little more.
“They made a beautiful goal – without good marking from our side – but after I think the team reacted very well.”
Manchester United manager Louis van Gaal:
“I feel we didn’t reward ourselves with a victory because we were the better team. Until the last quarter we played very well and could have scored more goals. But you have to control the game better and we did not do that.
“It isn’t a lack of concentration it is not being composed when you are defending. When we have the ball we have to keep the ball.
“You need to give the right pass at the right moment and we did not do that [before Chelsea scored]. Chelsea are a very good team and you play like we played and don’t reward yourself, it is frustrating.”