Cristiano Ronaldo scored his 17th goal of the season to earn Manchester United a point after David de Gea had frustrated Chelsea with several superb saves.
The visitors were thoroughly dominant in the first half at Old Trafford but were unable to find a way past De Gea, who made saves from Kai Havertz and N'Golo Kante.
But Chelsea finally broke the deadlock midway through the second half when Marcos Alonso volleyed home from an angle.
The Blues' celebrations had barely finished as Manchester United responded within a minute, Nemanja Matic playing a brilliant ball into the box and Ronaldo taking a touch before thumping a shot into the net.