In front of a crowd of 610 at Croft Park, Nathan Buddle opened the scoring with a terrific strike from 25-yards after 22 minutes.
Damen Mullen scored from a lot closer in to make it 2-0 in the 63rd minute.
But Ben McKenna reduced the deficit from the penalty spot in stoppage time to set up a nervy finale, but Blyth held firm to move up to ninth, two points behind the top seven, to keep their slim play-off hopes alive following Spennymoor United`s home defeat to AFC Telford United.
Blyth are optimistic as this was Spennymoor`s third straight defeat and although they have two home games against already-relegated North Ferriby United and a now safe Southport to come, all eyes will be on their results and the outcome of seventh-placed Bradford Park Avenue`s visit to Kidderminster Harriers on Saturday.
At the Brewery Field on Tuesday, Moors got off to a great start when Mark Anderson put them ahead after just 3 minutes.
The Bucks equalised on the half-hour mark when a poor backpass from Joe Tait finished with Marcus Dinanga sliding the ball home.
However, 10 minutes into the second half, the visitors went down to ten-men when a challenge deemed reckless by Dominic Smith on Bradley Fewster saw the Bucks man dismissed.
But it was the ten-men who eventually sealed victory in the 68th minute with a goal from 18-year-old Ryan Giles.
Tuesday`s other scheduled game between Nuneaton Town and Boston United was called off due to floodlight problems.
(DJ Nelson Photos)