Eddie Anaclet grabbed only his second goal of the season to help Oxford United to a fourth win in five away games.
The right-sided midfielder capitalised on not the best piece of goalkeeping from 18-year-old Josh Mimms to volley in from nine yards in the 48th minute.
It was Anaclet's first league goal of the campaign, his previous one coming when he came off the bench in United's 3-1 win at home to Northwich in the FA Cup.
Oxford defended well at KitKat Crescent against an under-strength York side, but as a match, it will not live long in the memory.
With Luke Foster suspended, Darren Patterson went for a 3-5-2 formation at the start, partnering Yemi Odubade and Matt Green up front for the first time, and recalling Jamie Hand into the midfield in place of Eddie Hutchinson.
York had four players suspended, and were forced into fielding two - Jimmy Beadle and Andy McWilliams - who had not played for the first team before.
Their bench resembled a nursery, with three youth-team players, in contrast to that of the visitors.
The U's made a positive start, and after good play by Eddie Anaclet, Adam Murray fired over a dangerous low cross from the right to test Mimms, son of Bobby, who was making his home debut.
York went close to opening the scoring on 14 minutes when Jamie Hand failed to close down Martyn Woolford quickly enough and the midfielder hit a stinging low drive from 25 yards that bounced just in front of Billy Turley. The keeper, five yards out, got his hand to it, and the ball remarkably flew over the bar.
Moments later, Leo Fortune-West turned Barry Quinn and shot narrowly wide from 15 yards.
Oxford struggled to create chances going forward, although Adam Murray was doign some excellent things in the centre of the park, always trying to get the ball down and keep possession where others simply tried to head it on.
For most of the first half, defences were very much on top, which meant it wasn't a very exciting spectacle.
This one really did have an "end-of-the-season can't wait for summer" feel to it.
Oxford soo changed to their more accustomed 4-4-2, though with the fullbacks still getting forward when they could.
Barry Quinn produced a great tackle on Emmanuel Panther on the edge of the box to stop one York attack.
Lanky striker Richard Brodie, playing wide left, drifted over to the right and got around the back of the U's defence, then cut back from the bye-line only to see his scooped shot deflect way over.
And from the corner, it needed a combination of Murray and Matt Day to get the ball away from the visitors' goalline, and prevent a goal.
It was just three minutes into the second half that United got the breakthrough they had been looking for.
Odubade instigated the attack with a sharp turn and run at defenders, which earned a corner on the left.
Michael Howard took it, Phil Trainer noodded it on, and as the ball bounced just in front of young keeper Mimms, Odubade went in and challenged for it with his head - and it deflected perfectly for Anaclet to volley in a simple shot in front of the away fans.
Craig McAllister replaced Green, who had been disappointing overall, midway through the second half.
As the game opened out in the second half, United put together some quick breaks. Odubade had a couple of lightning-quick runs, and Trainer's counter-attack set up a shot for Murray, who drilled a low 25-yarder narrowly wide.
Day got in a good block on the line when York forced a corner near the end, but overall the visitors were quite comfortable - and the win gives them a real chance now of finishing in the top half of the table.
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