Matty Longstaff put Newcastle in front after 17 minutes, firing into the bottom-left corner for his second goal against Man Utd this season.
Martial equalised midway through the first half, beating Martin Dubravka with a powerful strike.
Following a mistake by Fabian Schar, Mason Greenwood put Man Utd in front 12 minutes later with a thunderous effort in off the bar before Marcus Rashford headed in United's third on 41 minutes.
Martial made it 4-1 six minutes into the second half, capitalising on Sean Longstaff's underhit back-pass before being denied a first Premier League hat-trick by the post.
Man Utd have 28 points, three ahead of 10th-placed Newcastle.
Man Utd: 28 Dec v Burnley (A)
Newcastle: 28 Dec v Everton (H)