It was solid defensive display from both sides as the only real opportunities in the first 45 minutes from Martial, Romelu Lukaku and Martial again were thwarted in the final moments.
The defensive solidity continued in the second period with Lukaku denied early on but Martial put United ahead after 53 minutes. The game burst into life from there on in with chances from Phil Jagielka, Jesse Lingard and Jagielka once again but United had done enough to claim a pivotal three points.
After the tributes to club legend Sir Bobby Charlton before kick-off, both sides looked up for the contest but failed to produce any chance of any recognition until the 16th minute.
Martial has impressed in his first season in the English top-flight and he was at it again as he ran into the area from the chip of Lingard. The Frenchman had a crack on goal but the slight deflection from Leighton Baines took it wide of Joel Robles' right-hand post.
Lukaku is another player that has impressed throughout the campaign and looked to be through on goal in the 25th minute. He tried to capitalise on Chris Smalling's slip but David De Gea won the footrace as he sprinted off his line to clear any danger.
Martial was causing problems again, eight minutes from the break, as he combined with Marcus Rashford receiving the ball from the youngster's back-heel pass.
The Frenchman looked to be through on goal but John Stones, who had been heavily criticised of late, showed that he still had the credentials as he flew across with the sliding challenge to prevent the danger.
United proved tough to break down once again as the second half got underway as Baines played it low to Lukaku who looked to turn Daley Blind but the Dutchman, who had been brilliant to that point, was at it again to smother the Belgian's effort.
United had the better opportunities of the two sides and made it count as they tucked away the record-breaking opener in the 53rd minute.
It was great play from Rashford once again as his flick released substitute Timothy Fosu-Mensah who hooked a ball across the face of goal to the back post and Martial was there to notch United's 1000th Premier League goal at Old Trafford.
Burst into life
The opening goal from the Frenchman saw the game burst into life as Everton almost instantly had an equaliser.
Jagielka did well to get away from his marker Morgan Schneiderlin to get his head onto the end of a corner but his efforts weren't rewarded as it clattered the upright.
Louis van Gaal's side came within inches of doubling their lead as a byline cross from Juan Mata looked for Lingard but the England youngster was inches away from converting the Spaniard's pass.
Backs against the wall
It was a nervy final ten minutes for the home side as Roberto Martinez's side had two good opportunities to take a point.
The first came from Jagielka once again in the 82nd minute when he was presented with a chance but De Gea, who had been rarely troubled, did well to stop the point-blank effort from finding the back of the net.
Stones played an excellent through ball three minutes later into the feet of Seamus Coleman whose dangerous low ball looked for Lukaku at the face of goal but the Belgian just missed the ball and Fosu-Mensah's clearance secured the three points for United.