Substitute Schofield latched on to Luke Beckett's clever through pass and slipped the ball under goalkeeper Neil Moss to secure all three points for his side.
The win was Huddersfield's first away victory since October 21 and means Bournemouth have now lost two on the bounce.
Bournemouth had the first attempt on goal in a quiet opening into the game when Darren Anderton floated over a free-kick on ten minutes that midfielder Marc Wilson headed just wide.
Huddersfield opened the scoring barely a minute later when midfielder Jon Worthington robbed Bournemouth left-back Ryan Bertrand on the halfway line.
Worthington ran clear of the Bournemouth defence and smashed the ball home past goalkeeper Moss.
Bournemouth hit back through Stephen Purches who hit a left-footed shot from 20 yards that Matt Glennon did well to push out.
Huddersfield's veteran striker Andy Booth hit a 20-yard shot that Moss went down to push past the left-hand post.
Bournemouth equalised just before half-time with Purches' first goal of the season.
The right-back picked up the ball on the edge of the penalty area and pushed it through Martin McIntosh's legs before hitting a right-footed shot past Glennon and in off the far post.
Huddersfield almost took the lead just after the break when ex-England international Anderton lost the ball to Michael Collins just outside the area. Collins hit a 20-yard shot that had to be tipped over the bar by Moss.
Huddersfield substitute Schofield went close with a rasping 25-yard free-kick that whistled past the post on 78 minutes before hitting the winning goal seven minutes later.
Bournemouth substitute Steve Fletcher missed a golden opportunity to equalise for his side deep into injury-time.
Fellow substitute James Lawson swung over a cross that Fletcher headed downwards from eight yards out, but Glennon dived to his left to gather the ball and secure all three points for his side.