Kayode Odejayi pounced for his sixth goal of the season in the 18th minute with a cool finish after Ryan Clarke had saved from James Gray.
Oxford felt Gray had fouled Michael Raynes in the build-up to the goal, but the referee was not interested.
Stanley doubled their lead when Gray ran through some weak challenges to drill a low angled shot past Clarke nine minutes into the second half.
U’s striker James Constable, desperate for one more goal to equal the club’s all-time goalscoring record of 107 goals, went close a couple of times to finding the net.
Australian winger Ryan Williams pulled a goal back for Oxford by firing in a low shot in a crowded box in the 67th minute but they were unable to find a leveller.
Instead it was Stanley who threatened a third, but Clarke saved well from Will Hatfield in the dying stages.
Oxford’s collapse this season, from leading the division to missing out on the play-offs, has been staggering and they were booed off at the final whistle by their supporters.