Henrikh Mkhitaryan's breakaway effort secured an identical result in this fixture last season after Spurs had dominated possession and it was a similar story here as Mauricio Pochettino's men struggled without injured talisman Harry Kane.
The England man was absent with a hamstring problem, Pochettino choosing Son Heung-min over Fernando Llorente in attack, but Pep Guardiola's branding of Spurs as "the Harry Kane team" may be revisited after they failed to break down United's stiff defence.
Any suggestion that Jose Mourinho would throw the shackles off after soporific attacking displays in a draw at Liverpool and defeat at Huddersfield Town were quelled as the Portuguese matched Spurs up with a three-man defence.
But the Red Devils grew into the contest, and Romelu Lukaku hit the post late on before his flick-on sent Martial clear to score nine minutes from the end and reassert United in second place, now three points above their visitors.
United needed a response after turgid performances at Anfield and Huddersfield, but Mourinho's approach was suitably cautious and Lukaku was left badly isolated in attack, spooning an early chance out for a throw-in, while Marcus Rashford hit United's only shot on target of the first half from a 30-yard free-kick that Hugo Lloris comfortably tipped wide.
Spurs tentatively limited themselves early on to pot-shots from distance - Serge Aurier, Moussa Sissoko and Toby Alderweireld could not test David de Gea - but the goalkeeper found Phil Jones more of an obstacle, dropping a cross on his team-mate's shoulder to present Sissoko a chance that ballooned into the Stretford End.
The visitors began to make good ground out wide, a ploy that cried out for Llorente's presence in the box, but De Gea was brought into easy action twice more before the break by Dele Alli and Eric Dier.
Only a brilliant intervention from Ben Davies denied Rashford after Lloris spilled Mkhitaryan's shot back into danger, but the skipper redeemed himself when turning the Armenian's cross out of Lukaku's path.
Pochettino summoned Llorente and Mousa Dembele shortly after the hour mark as increasingly persistent rain began to swirl Old Trafford, Antonio Valencia the next to go close to lifting the gloom when he fizzed over from 18 yards.
It was Mourinho's introduction of Martial in Rashford's place that would change the game, but Spurs wasted a gilt-edged chance when Christian Eriksen's ball over the top picked out Alli, who could only scuff wide under pressure.
Substitute Jesse Lingard crossed for Lukaku, who planted a header against the foot of the right-hand post, but the Belgian's next touch with his head set up the winner.
De Gea's long kick down the field was flicked on by Lukaku into the path of Martial, who raced clear of Dier and smashed home left-footed.
United's home form moves onto five wins from as many games without conceding and though the style of many of them was missing here, the substance outlines them and Mourinho as title candidates still.
10 - @ManUtd have now scored 10 goals in the last 10 minutes of PL games this season, accounting for 43% of their total. Patient.— OptaJoe (@OptaJoe) October 28, 2017
Key Opta stats:
- Manchester United have kept a clean sheet in each of their first five home league games of a season for the first time since 2007-08.
- Tottenham have lost consecutive games (in all competitions) for the first time since February (defeats against Liverpool and Gent).
- Anthony Martial has been involved in five goals in his last five Premier League games at Old Trafford (three goals, two assists).
- Romelu Lukaku has had a hand in 10 goals in the Premier League this season (seven goals, three assists), a joint-high along with Sergio Aguero.