There was little between the teams on this occasion and one goal always looked likely to decide it.
Having defended brilliantly all afternoon, we were undone by a route one goal nine minutes from time. David de Gea launched a free-kick long, Romelu Lukaku flicked on and Anthony Martial got in behind to finish.
That was just minutes after our best chance as Dele Alli touched Christian Eriksen's pass wide from close range. Lukaku hit the post after that and the game looked destined for 0-0 until Martial struck.
The result ended our run of six successive away wins and was our first loss on the road this season - United have won five out of five at home.