The Blues cut United’s lead at the top to just two points, with a virtual title decider awaiting the pair on April 26 at Stamford Bridge.
Michael Essien’s 41st-minute strike was enough to smother Everton’s hopes, with the Toffees now five points behind Liverpool in fourth.
It took until four minutes before the break for Chelsea to take the lead.
Neat passing involving Salomon Kalou, Essien and Shaun Wright-Phillips ended with the ball deflecting off Phil Jagielka, straight into the path of Essien who lifted the ball into the top corner.
Everton improved after the break and Manuel Fernandes was inches away from a 67th-minute equaliser only for his free-kick to flash the wrong side of the post.