Salisbury struck early to record their first win in seven league games and stay clear of the relegation places.
Charlie Griffin nodded home Liam Feeney's inswinging corner in the fourth minute.
Feeney's left-wing cross then provided a close-range finish for Charles Ademeno that doubled the lead.
Sam Deering drilled home a left-footed shot after the interval for Oxford but, although Yemi Odubade later went close to an equaliser, Salisbury held on.
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