Having reportedly rejected United's initial offer of a new contract, Martial ensured the week ended with the focus firmly on his talents as he created United's first and scored the second in a scintillating display.
The 22-year-old won the penalty that Paul Pogba converted at the second attempt in the 27th minute before lashing home what proved the winner just after half-time.
Chris Smalling, on his 300th United appearance, made their task more difficult than it should have been when his rash challenge allowed Gylfi Sigurdsson to halve the deficit from the spot, but the hosts held firm to quickly move on from their limp Champions League loss to Juventus in midweek.
Romelu Lukaku's omission from the starting XI afforded Martial a prominent role and it was his quick feet that drew the penalty from Idrissa Gueye, who did get a toe to the ball before the attacker's theatrical fall.
Jordan Pickford impressively kept out Pogba's initial effort, but the midfielder's stuttering run-up was spared from more scrutiny as he rolled in a fortunate rebound.
It was a role reversal for United's second as Martial gloriously curled a Pogba pass into the bottom-right corner within four minutes of the restart.
Bernard passed up a chance to drag Everton back into it before Smalling's tackle enabled Sigurdsson to grab a consolation from the spot in the 77th minute.
The margin should ultimately have been greater but Martial finally let his standard slip in the 94th minute, failing to beat Pickford in a one-on-one.
What does it mean? Plenty of life without Lukaku
Lukaku, dropped after an eight-game scoreless streak, might find himself on the bench more regularly after Martial and Rashford proved United can pose problems without their first-choice centre-forward. The Frenchman has four goals in his last four appearances and should have scored again in stoppage time.
Pogba guides United's path
His penalty-taking method must rankle with pragmatist Mourinho and a loose pass led to the Toffees' goal, but Pogba was so often at the heart of United's best moves and in this mood his manager will accept the good with the bad.
Bernard in the bad books
Muted for much of the hour he was on the pitch, Bernard's failure to make the most of a golden opportunity soon after Martial's strike denied Everton greater hope of snatching a point.
Key Opta Facts
- United have scored 100 Premier League goals against Everton, more than they have managed against any other side.
- Everton are without a win in their last 30 Premier League away games against the 'big six' (D9 L21), since a 1-0 victory at Old Trafford against United in December 2013.
- Paul Pogba has been involved in 31 Premier League goals since the start of 2016-17 (14 goals, 17 assists); more than any other United player.
- Everton's Sigurdsson has scored four goals against United in the Premier League; against no side has he scored more often.
United have time to prepare for a difficult excursion to in-form Bournemouth on Saturday, while Everton host Brighton and Hove Albion on the same day.