The visitors, who have had a positive start to the campaign themselves and of course beat Liverpool 7-2 earlier in the season, gave as good as they got and briefly pulled level in the second half, with Bertrand Traore slamming home to cancel out Anthony Martial's opener.
But Bruno Fernandes converted a spot-kick awarded for Douglas Luiz's foul on Paul Pogba, and the Reds held out for all three points.
Who was our standout performer, though?
David De Gea was a contender, with the Spaniard making four saves in total, including from Ollie Watkins's goalbound header and Matty Cash's rasping late drive.