Second-half strikes from Matthew Jarvis and debutant Dean McDonald put the Gills in control before Gary Fletcher-Taylor's 81st minute strike set up a tense finish.
Gillingham began the game strongly and carved out the first clear opening on 18 minutes when Jarvis found space in the area before seeing his shot bravely blocked by Martin McIntosh.
Gillingham's new signing, McDonald, began to cause problems for the Town defence and in the 29th minute produced some neat trickery in midfield before firing a 25-yard drive narrowly wide of Matthew Glennon's right-hand post.
On the stroke of half-time, Gillingham produced their best opening of the game. Duncan Jupp's deep cross was met with a firm header by fellow debutant Mark Bentley, bringing a point-blank save out of Glennon.
Gillingham continued to dominate after the break and in the 57th minute got the opener their pressure deserved. McDonald and Brent Sancho combined to win the ball in midfield before releasing Jarvis who held off Andy Holdsworth's challenge to beat Glennon at his near post.
The Gills nearly doubled their lead only moments later when a weak back pass allowed Bentley in only to see the ball deflect over the bar off his shins.
Schofield almost restored parity soon after when he latched onto Luke Beckett's throughball and held off the challenge of three defenders before forcing Kelvin Jack to save.
Gillingham doubled their advantage in the 67th minute. Gary Mulligan found McDonald on the edge of the six-yard box and the youngster swivelled on a sixpence before firing an unstoppable shot past the hapless Glennon.
Beckett missed an immediate chance to reduce the deficit, but in the 81st minute substitute Pawel Abbott's clever chip forced Jack into a save and Taylor-Fletcher was on hand at the far post to tap home.
Huddersfield now sensed a chance to take something from the game and almost snatched an equaliser when Taylor-Fletcher's through ball put Chris Brandon through on goal but he opted to shoot when a cross seemed the better option
It was to prove the final scare for Ronnie Jepson's side, who hung on for the three points.