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Victory saw United, who had started the day ahead of Spurs on goal difference alone, go three points clear of their London rivals.
France international Martial, currently battling to win a regular starting place under Jose Mourinho, did his chances no harm with the manner of his 81st minute winning goal, even if it was a curiously direct affair.
A long kick forward by goalkeeper David De Gea was headed on by Romelu Lukaku and Martial sprinted away from the Spurs back line before calmly beating the keeper with an excellent finish.
It was a disappointing way for Spurs to lose a game and the fact that the London club were without injured leading striker Harry Kane is bound to revive the debate over whether their bid to be crowned champions is too reliant on the England forward.
After being widely criticised for their negative approach in the recent goalless draw at Liverpool, United showed more ambition against another of the division’s top clubs on their own turf, although the result was still a lack of real goalscoring chances and entertainment.
Within two minutes, Lukaku chased onto a through ball and his low, driven cross-shot was well cut out by the alert Hugo Lloris, with Marcus Rashford poised in the middle in front of an open net.
Ashley Young’s penetrating run might have carved out a chance but his drag-back passed through the area and narrowly out of reach of three team mates before a 35-yard Rashford free-kick was turned around the post by the diving goalkeeper.
Spurs, understandably given the absence of Kane, adopted a more cautious approach but grew into the game as the half progressed.
Early chances were limited to long shots — Serge Aurier and Moussa Sissoko forcing De Gea into simple stops and Toby Alderweireld shooting into the side-netting from outside the area.
But by the time Christian Eriksen floated over a delightful pass in the direction of Dele Alli, who was denied the chance to volley on goal by two defenders, Spurs looked comfortable.
When Tottenham did create a real chance, it was in bizarre circumstances as De Gea made a routine catch from a Ben Davies cross but collided with Phil Jones and dropped the ball.
– Young and Alli clash –
Alli was alert and passed the ball back to Sissoko who fired well over the crossbar from the edge of the area.
Soon, Young and Alli were involved in an altercation, after the United man was accidentally hit in the face by Aurier, with players from both teams squaring off in an incident which breathed much-needed life into the game.
Tottenham reacted first as Alli saw his header, from a Davies corner, blocked by Eric Bailly and then the England midfielder found space for a shot which failed to trouble De Gea.
Another Davies corner again caused problems before De Gea caught Eric Dier’s hooked shot towards goal.
United opened the second half in more committed fashion and, finally, after 54 minutes, the home crowd had something to cheer as the Reds created three quick chances in succession.
A mistake by Davies presented Henrikh Mkhitaryan with an opportunity for a shot which Lloris fumbled. But for Davies atoned for his error with a superb cover-tackle to deny Rashford a simple goal from the rebound.
The attack continued with Ander Herrera setting up Antonio Valencia, whose shot was blocked.
Lukaku then shrugged off Jan Vertonghen before sending a low shot just wide of the goal.
Both teams had chances to break the deadlock shortly before Martial scored the only goal of the game.
Alli flicked agonisingly wide after a brilliant chip forward from Eriksen and Lukaku headed against the post from Jesse Lingard’s cross.
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