Ole Gunnar Solskjaer’s side backed up their win against Newcastle on Boxing Day, but found life much more difficult at Turf Moor.
The Clarets failed to unsettle United throughout, but United failed to cut through them with the ease displayed two days ago against the Magpies.
David de Gea’s fine save in the second half kept Burnley out before a late counter saw Rashford add a second.
Here are the player ratings from Turf Moor.
Who was your man of the match?
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