In front of another terrific crowd of 3,423, Matty Warburton gave County the lead on the half-hour mark.
But Spartans were level within 3 minutes through Adam Wrightson.
However, it wasn`t until right at the end of the game that the visitors pulled clear when Michael Liddle put them in front in the 89th minute and then Jarratt Rivers added a third in stoppage time.
Blyth`s north-east rivals Spennymoor Town are now three points behind in fourth after losing 4-2 at the Brewery Field to a Curzon Ashton side who are now eighth.
Moors led 2-0 with goals from Mark Anderson after 17 minutes and Glen Taylor 6 minutes later.
But the game turned on a penalty decision 3 minutes after half-time when the home side`s Chris Mason was shown a second yellow card for the offence and Niall Cummins scored from the spot.
On 66 minutes, Cummins again pulled the Nash back on level terms and 3 minutes later he completed his hat-trick.
Ben Wharton made the points safe with a fourth for the visitors with 12 minutes to go.
The third north-east side in the league, Darlington FC, suffered a 2-1 defeat at Liberty Way against struggling Nuneaton Town.
Ashley Chambers gave Boro the boost of an early 8th minute lead.
A minute after half-time, Jordan Nicholson doubled the home side`s lead, with all the Quakers could muster being a last-gasp David Syers effort.
York City threw away two points at Leamington after squandering a 2-0 lead 5 minutes from time.
The Minstermen looked to be cruising following David Ferguson’s first goal for the club after just 9 minutes and Jon Parkin’s 9th of the season in the 53rd minute.
But Junior English 5 minutes from time and Liam Canavan 3 minutes later earned the hosts a battling point and denied new York boss Martin Gray back-to-back wins from his first two games in charge.