The game burst into life in the 24th minute when County's Julian Kelly presented Bury skipper Stephen Schumacher with the ball 25 yards out and his spectacular effort put the visitors ahead.
County levelled after 58 minutes when John Cofie played a terrific ball through to Kelly who cut inside and placed his finish past Trevor Carson to atone for his earlier error.
The Magpies were ahead in the 61st minute when Zoko bullied Bury defender Ashley Eastham off the ball in the box and slid the ball into the bottom right-hand corner.
A revitalised County extended their lead after 65 minutes when Zoko made the most of poor Bury defending to round Carson and roll the ball into an empty net.
The game was over as a contest after 74 minutes when Eastham tripped Alan Judge in the penalty area and Jamal Campbell-Ryce sent Carson the wrong way from the spot.