The French striker was restored to the starting line-up at Old Trafford by Jose Mourinho as Manchester United extended their unbeaten run in the top flight to 16 games.
Juan Mata gave the Red Devils the lead in the first half when he finished from close range after being found by Martial.
And Martial then doubled the home side’s advantage in the second half when he scored a confident finish after being set free by Zlatan Ibrahimovic.
It was only Martial’s 10th Premier League start of the season under Mourinho after struggling to find consistent form this term.
And speaking to BBC Sport after the game, former Arsenal defender Keown said: “Martial has been pressurised by his manager and that’s pleasing, because he’s a great talent but he needs to start to show that in a United shirt.
“But now he’s scored, and that will do his confidence a world of good.”
The victory lifted Manchester United up to fifth place in the Premier League table ahead of Liverpool’s clash with Tottenham at Anfield.
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