The Frenchman was introduced as a second-half substitute and rounded off the scoring at Old Trafford to give Louis van Gaal's men all three points against their bitter rivals
Daley Blind opened the scoring early in the second half and then saved his side at the other end with a tremendous goal-line clearance before Ander Herrera won and converted a penalty to put the hosts two up.
David de Gea, who signed a new contract this week, could do nothing to stop a stunning Christian Benteke overhead kick on his return to the starting line-up following the collapse of his move to Real Madrid before new signing Martial marked his debut by coming off the substitutes' bench to seal the points with an excellent solo goal.
The result meant United inflicted a second consecutive loss on Liverpool, while Louis van Gaal's side move up to second in the early-season table.
Simon Mignolet gave the travelling fans an early moment of panic by directing a throw straight at Juan Mata. The midfielder fed stand-in striker Marouane Fellaini, who was playing in place of the injured Wayne Rooney, but his long-range chip was well over the crossbar.
Poor control from Fellaini meant the rare opportunities United had in Liverpool's area came to nothing, while Liverpool struggled to provide their lone striker, Benteke, with any kind of meaningful service as neither side registered a shot on target in the first half.
Van Gaal made a half-time change with Ashley Young replacing Memphis Depay and the former Aston Villa winger made an immediate impact, winning a free-kick from Nathaniel Clyne on the edge of the box.
Mata took it, cleverly cutting a pass back to the 18-yard line where an onrushing Blind was unmarked. The centre-back took full advantage of the space, curling a sumptuous left-footed strike into the top corner.
A timely intervention from Chris Smalling gave United a let-off after De Gea's scuffed clearance had presented Liverpool with a rare opening at the other end before the Spain goalkeeper made amends with a sprawling stop to divert Danny Ings' bouncing effort away from goal after a free-kick had deflected into the forward's path.
Brendan Rodgers' side were starting to become more threatening and Blind had to make two frantic clearances from the goal-line after Martin Skrtel had headed on a James Milner corner to cause a mad scramble.
Any hopes of a Liverpool comeback were seemingly ended, though, when United won a penalty. Michael Carrick fed Herrera, who was felled by a Joe Gomez challenge in the box. The midfielder stepped up to take the resulting spot-kick himself and smashed his effort into the roof of the net.
Milner shot narrowly over with a free-kick and Benteke headed over the crossbar from a decent chance as the away team attempted to respond before De Gea was called into action again with a diving stop to deny substitute Jordon Ibe.
Liverpool continued to press and had hope of a late recovery when Benteke produced a stunning overhead kick after an Ibe cross deflected into his path.
But those hopes were dashed when Martial went on an excellent solo run, beating Skrtel and converting a cool finish into the far corner to mark his debut in style.