Schofield's goals were the highlight of a dull match which seemed set for a 0-0 draw before his late goal sealed the points for the Terriers.
The ice-breaker was an sweet 82nd minute right footed curling shot which beat Paddy Kenny and went in off the inside of the Bury post after Andy Booth had put the youngster through.
Sam Collins could have equalised for Bury three minutes later when poor Town marking from a corner allowed Andy Preece to knock the ball down for the former Town defender whose effort rebounded off the outside of Martyn Margetson's post.
The nerves were there until the the 88th minute when Andy Booth blocked an attempted clearance by a Bury defender and let the ball run to Danny Schofield on the edge of the area.
Paddy Kenny was off his line and Schofield fearlessly lobbed the helpless 'keeper from 20 yards to seal the points for Town.
The action in the last 10 minutes made up for a very dull first 80 minutes in which John Thorrington showed flashes of the attacking pace and skill which caused Bury, and Chris Armstrong in particular, problems down Town's right flank.
Thorrington made a habit of beating Bury defenders and had one or two chances on goal himself along with hands in half chances for Craig Armstrong and Andy Booth but Bury were a little more organised in defence than Town.
The Terriers defence could have let them down again, though, as Gareth Seddon should have capitalised on three clear attempts in the first half where he found himself unmarked and in a decent shooting position but somehow conspired to miss each one.
The overall Town performance against a reasonably organised Bury side was forgettable, but the result was welcome.
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Town (4-4-2): Margetson, Heary, Jenkins, Gray, Thorrington, Holland, Armstrong (Mattis 56), Evans, Booth, Schofield, Hay (Beech 83)
Subs not used: Digby, Moses, Irons
Scorers: Schofield 82, 88
Bury (3-5-2): Kenny, Unsworth, Armstrong, Redmond (Jarrett 83), Collins, Nelson, Billy, Forrest (Bullock 78), Reid, Newby, Seddon (Preece 56)
Subs not used: Swailes, Murphy
Booked: Unsworth, Armstrong
Attendance: 8684 (767 away fans)
Referee: Graham Laws (Whitley Bay)