Martial curled the ball into the net from the edge of the area to break the deadlock before Lingard also bent a shot beyond Jordan Pickford from distance.
Juan Mata hit a post for United while Oumar Niasse spurned Everton’s best chances.
The win ends United’s run of three straight draws, while Everton, now without a win in four, stay ninth.
United looked to be close to their best in the second half, with Paul Pogba providing the assists for both goals.
Lingard’s stunning strike was his seventh in the league this season, all scored in nine appearances since 28 November.