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Harris struck in the 35th minute, slamming in Siriki Dembele’s low cross following a pacy break down the left.
The win extended Oxford’s unbeaten run to eight games and was a first defeat in seven for Stockport.
The Hatters were without Adama Sidibeh – who came off the bench to earn a point at Notts County – because of a thigh injury.
Top scorer Kyle Wootton headed Benony Andresson’s left-wing cross over from 10 yards and Andresson was denied by a smart save from Jamie Cumming as the visitors started to boss proceedings for a while.
But Harris’s goal changed the mood, and Louie Sibley then Harris again almost struck again before half-time.
In the second half, with Oxford on top, Dembele shot straight into Oliver Whatmuff’s arms and the County keeper kept out a ferocious Cameron Brannagan free-kick.