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The loss leavesFulham on the edge of the relegation zone in 17th place, while Arsenal move up to third.
Manchester City winger Riyad Mahrez missed an 86th minute penalty as the Premier League champions were held to a 0-0 draw at Liverpool in their top of the table clash.
The result left United sixth on 32 points from 19 games halfway through their campaign.
Unbeaten Liverpool have 45 points from 17 games with champions Manchester City, who beat Everton 3-1 on Saturday, a point behind.
Harry Kane scored twice, including a penalty, as Tottenham Hotspur inflicted further woe on bottom-placed Huddersfield Town.
Despite their defeat, Leicester impressed and had more possession and shots on target than Liverpool.
Two first-half goals from Romelu Lukaku were enough for 10-man United to beat Burnley 2-0 at Turf Moor.
Bournemouth and Everton maintained their unbeaten starts to the season in a dramatic match in which both sides ended with 10 men.
United have lost two of their opening three games of the season and conceded six goals in the last two games.
It was an accomplished performance from Juergen Klopp's side who, looked solid at the back as well as a threat going forward.
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