The three points took United past West Ham into fifth position on the log, just one behind “noisy neighbours” Manchester City with seven games to go in the season.
And it was 20-year-old Frenchman Martial who provided the only goal of the game in the second half.
After a dour opening 45 minutes when there was hardly a shot on goal, the game came alive following the break when Juan Mata found Marcus Rashford on the edge of the Everton box, and the young English striker flicked the ball into the path of a flying Timothy Fosu-Mensah, who had replaced Marcos Rojo at halftime.
The Belgian defender delivered the perfect ball across the face of the Everton goal and it had just enough speed to beat Seamus Coleman at the back post, with Martial finishing in style for a crucial score in the 54th minute.
The goal delighted United legend Sir Bobby Charlton, who had been honoured before kickoff for 60 years’ service to the club by having a stand named after him.
Everton captain Phil Jagielka had two huge chances to equalise, the first a free header from a corner two minutes after Martial’s strike, which hit the crossbar.
The second came with around seven minutes to go when the ball fell to Jagielka inside the United box, and his shot was well-saved at point-blank range by the Red Devils’ goalkeeper David de Gea.
There was one last opportunity for the visitors when it looked like in-form striker Romelu Lukaku would slide in for the equaliser, but he just couldn’t get a final touch to it and Fosu-Mensah swept the ball away from danger.
United manager Louis van Gaal would’ve breathed a sigh of relief, as the triumph meant that they are still in the running for a Champions League spot by ending in the top four as they look to overhaul their great rivals Manchester City.
Earlier on Sunday, log-leaders Leicester City increased their advantage to seven points at the top of the Premier League with a 1-0 victory over Southampton at the King Power Stadium, with Wes Morgan netting the winner.
Premier League Top 6
1 Leicester City – Played: 32, Points: 69
2 Tottenham Hotspur – Played: 32, Points: 62
3 Arsenal – Played: 31, Points: 58
4 Manchester City – Played: 31, Points: 54
5 Manchester United – Played: 31, Points: 53
6 West Ham – Played: 31, Points: 51
Original source: Martial keeps United’s dream alive