Cambridge climbed into the Blue Square Premier league play-off places thanks to an own goal from York's Ben Purkiss.
The home side went in front six minutes into the second half when Felino Jardim whipped in a cross that Purkiss could only divert past his own keeper.
Cambridge continued to press, but Mark Beesley had a number of goalbound efforts blocked.
The visitors almost grabbed an equaliser when Craig Farrell's header thumped against the post.
Cambridge Utd:
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Booked: Carden.
Goal: Purkiss 51 og.
York:
Booked: Kelly, Greaves.
Att: 2,914
Ref: J Hopkins (Wickford).
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