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 the 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 UEFA 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.
United has time to prepare for a difficult excursion to in-form Bournemouth next weekend, while Everton hosts Brighton and Hove Albion.