Hume tapped home from Scott Laird's low cross in the 74th minute at Meadow Lane to finally break the Magpies resistance.
Callum McGregor and Adam Coombes both went close for the hosts but Chris Kiwomya's side could not find an equaliser as they slumped to their third defeat in a row.
In a bad-tempered first half, Greg Tempest was denied by a smart Declan Rudd save, while at the other end Stuart Beavon's long-range effort was palmed away by Fabian Spiess.
Celtic loanee McGregor had a great chance for County after the break but fired high, while Coombes' header brought another fine save from Rudd.
Substitute Hume made the Magpies pay for not taking their chances, slotting home after fine work by Laird.
Hume came close to doubling his tally late on while Keith Keane also forced a save from Spiess as the promotion chasers finished on the front foot.