Diego Costa scored a late equaliser to preserve Chelsea's unbeaten record under interim boss Guus Hiddink and deny Manchester United a win.
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.
A United performance to offer encouragement
This will feel like a defeat for United after a bright start and a wonderful goal to give them the lead in what was an entertaining draw between two teams struggling for form.
Apart from the late equaliser, Louis van Gaal's side produced a display full of positives after recent criticism about the team's style.
They started well and offered more zip and energy than their cumbersome hosts.
Courtois' flying save to keep out Martial's curling attempt was excellent, while United forced 10 corners before the end of the first half.
The visitors looked set for a rare win over Chelsea when Lingard displayed terrific balance and agility to break the deadlock with a sublime spin and shot inside the area.
However, United's failure to hold out cost them dear, Costa pouncing from close range after a terrific Fabregas pass, and they now find themselves six points behind the top four.
Source: BBC