York 1-2 Barnet
Barnet aided their hopes of survival by coming from behind to beat York.
The Minstermen broke the deadlock in the seventh minute when Michael Rankine flicked in John McGrath's free-kick.
Keeper Graham Stack then saved smartly to prevent Matty Blair from doubling the hosts' advantage, before Andy Yiadom poked home the equaliser.
And the visitors completed the comeback - which moves them two points clear of the drop zone - when substitute Jake Hyde fired low past Michael Ingham.
VIEW FROM THE DRESSING ROOM
York City manager Gary Mills told BBC Radio York:
"It's a blow. It's another game we've lost.
"We're not winning football matches, it's another team below us that have just gone and beat us so it's a big blow.
"We've been giving goals away for quite a few games now for quite a few weeks.
"We haven't scored in abundance, we know that's a problem as well. But if you're going to concede like goals like we're conceding at this moment in time, it's just going to make it very very difficult."