The former Torquay forward scored the eighth-minute winner against the run of play following a quickly taken free-kick.
County playmaker Adam Chapman put Zebroski in on goal with an inch-perfect pass and the striker was aided by a looping deflection off right-back Dale Tonge as he slid in to try and stop the shot.
United left-back Kevin Nicholson nearly levelled from a 10th minute free-kick which flew just over and recalled Billy Bodin flashed another pacy free-kick just inches wide in the 24th minute.
United were reduced to 10 men in the 35th minute when winger Shamir Goodwin was sent off for a foul on County skipper Michael Flynn.
Martin Rice made a double save to deny Flynn and then Danny Crow, who followed up, in the 44th minute.
Left-back Andrew Hughes came closest to making it 2-0 when his header came back off the post in the 74th minute, just seconds after right-back Tom Naylor's audacious 50-yard chip was flapped over the bar by the back-pedalling Rice.