Everton, on the other hand, have now fallen to back-to-back defeats for the first time since October and see their five-match unbeaten home streak in the league come to an end following a toothless display on Merseyside.
United started Martial through the middle in the absence of injured duo Romelu Lukaku and Zlatan Ibrahimovic, while Everton welcomed back United legend Wayne Rooney as one of seven changes made to their starting lineup.
It was one of those changes who had the first opening too, with Mason Holgate rising highest inside the penalty area but sending his header well over the bar.
It proved to be one of the more notable attacking moments of a largely uneventful first half, although Everton's best chance arrived midway through the opening 45 minutes when Oumar Niasse broke into the box only to be thwarted by a fine last-ditch Marcos Rojo challenge.
The closest either side came to breaking the deadlock in the first half saw Paul Pogba cut onto his left foot and curl a shot towards the bottom corner which took a slight deflection on its way narrowly wide.
Lingard also threatened moments later with a low strike across goal which went wide of the far post, but a half-time scoreline of 0-0 was fitting for the pedestrian nature of the first half.
The visitors came even closer to breaking the deadlock five minutes later when Mata again found space to have a go from range, with his spectacular strike swerving away from Pickford but clipping the outside of the post on its way behind.
Pogba was the next to threaten when he broke in down the left channel before sending a low cross/shot past the far post, but United did finally break the deadlock shortly before the hour mark.
Pogba was again involved as he fed the ball to Martial, who curled a pinpoint finish into the top corner from the edge of the box to leave Jordan Pickford no chance.
It was Pogba who continued to look the most likely to create a second goal as the second half wore on, stinging the palms of Pickford following some dazzling footwork on his way into the box.
Everton did finally put up some resistance as the match entered the final 20 minutes, but Niasse nodded the home side's best chance narrowly wide of the target before Tom Davies saw an effort blocked from a promising position shortly afterwards.
It looked as though Lingard may have put the game beyond the Toffees in the 78th minute when his powerful low strike seemed destined for the bottom corner, but Pickford reacted well to get down and turn it round the post.
Lingard would only have to wait three more minutes to double his side's lead, though, continuing his recent purple patch in style by cutting inside from the right flank and curling his finish into the same corner as Martial, via a slight deflection off a defender.
Everton almost helped themselves to a consolation goal in stoppage time when Michael Keane nodded wide against his former club, but ultimately the hosts fell to their 35th Premier League defeat at the hands of Manchester United, which is more than any other team has suffered against a single opponent in the competition's history.
United, who will now sit second until at least Wednesday when Chelsea take on Arsenal, have also kept their first away clean sheet in eight attempts and close the gap on leaders Manchester City to 12 points.
Attention will turn to the FA Cup third round later this week, with both sides in action on Friday night when United take on Derby County and Everton face local rivals Liverpool in a Merseyside derby.
Everton (4-2-3-1): Pickford; Holgate, Keane, Williams, Martina; Davies, Schneiderlin, Vlasic, Rooney (McCarthy, 62'), Bolasie (Lennon, 62'); Niasse (Calvert-Lewin, 81')
Man Utd (4-3-3): De Gea; Lindelof, Jones, Rojo, Shaw; Herrera, Matic, Pogba; Mata (Tuanzebe, 92'), Martial (Rashford, 77'), Lingard (Blind, 87')