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.