James Constable scored the only goal as Oxford boosted their chances of playing their play-off semi-final second leg at home with victory over Altrincham.
Constable scored his 21st goal of the season early in the second half by heading home Adam Chapman's corner.
United were the better side and Constable forced a fine save from Stuart Coburn as he bid to make it 2-0.
Alty pushed for a leveller but Rob Williams was unable to beat U's keeper Ryan Clarke with his free header.
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