Martial, a 36 million pounds signing from Monaco this month, danced past three defenders in the 86th minute and sidefooted the ball home on his debut to put the finishing touches to a well-deserved victory.
After a dire first half that would have dampened the enthusiasm of even the most die-hard fan, a fired-up United emerged after the break to take the game by the scruff of the neck.
Daley Blind curled them ahead from the edge of the area four minutes after the restart before Ander Herrera slammed a penalty into the roof of the net after Liverpool's 18-year-old full back Joe Gomez clumsily felled the Spaniard.
Liverpool hit back with six minutes remaining when Christian Benteke pulled off an acrobatic overhead kick but he was spectacularly upstaged when Martial, a second-half substitute, had the United fans drooling in anticipation of his potential.
The result gave second-placed United 10 points from five Premier League matches, five adrift of leaders Manchester City.
Liverpool are three points further back after a match that exposed some familiar defensive flaws as well as a lack of attacking spark.
Pundits and fans alike had questioned the huge fee United paid for Martial, a 19-year-old who Van Gaal said was signed more for the future than the present.
For those who did not know a lot about him, including United striker Wayne Rooney, missing from Saturday's match through injury, the Frenchman announced himself in dynamic fashion.
United, however, were already in the box seat before he arrived on the pitch in the 65th minute.
Blind's brilliant finish brought the fixture to life after a first half when United hogged possession but had nothing to show for it.
The Dutchman shot home when a Juan Mata free kick from the left was cut back into his path.
United doubled the advantage with 20 minutes remaining when Gomez showed his inexperience, diving into a clumsy tackle on Herrera.
Herrera's penalty looked like being enough for United but Benteke's memorable effort gave Liverpool brief hope before Martial's moment of magic stole the show.
(Reporting by Toby Davis,; editing by Tony Jimenez)
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