Church, who scored once in seven appearances for Town last season, plundered the only goal on 54 minutes from a defensive blunder.
Oscar Gobern gave the ball away and Lawrie Wilson pounced to leave Church in the clear for a side-footed finish from close range.
Huddersfield had won their three previous meetings with Charlton, starting with an FA Cup third round victory last January.
This season Town beat the Addicks in a home double header - 3-2 in the Capital One Cup and 2-1 in the league.
Charlton's hopes of avoiding a fourth defeat in just 12 months were delivered a blow before the game with eight-goal top scorer Yann Kermorgant ruled out.
The target man, rumoured to be a transfer target for Celtic, scored twice against Oxford in their third round FA Cup replay last week.
But their chances improved when fisticuffs proved to be the main highlight of an otherwise drab first half.
Players from both sides faced off after Charlton midfielder Dale Stephens went in late on Huddersfield's Adam Hammill on 29 minutes.
Stephens was booked for the foul while Town's Anthony Gerrard and Addicks defender Michael Morrison saw yellow for their roles in the scrap which followed.
Just minutes earlier Huddersfield's Danny Ward was lucky to escape a booking for leaving his foot in on Cedric Evina.
The Charlton full-back and Hammill were both injured and had to be substituted with the tension simmering.
It came close to boiling over when Stephens brought down Oliver Norwood soon after but the former Oldham player escaped with a warning.
Ward was denied a goal on 26 minutes by keeper Ben Alnwick's smart parry after Paul Dixon put him through.
Striker James Vaughan, making his first start after five games out injured, had a shot blocked after a neat one-two with Gobern.
Town wing-back Tommy Smith retrieved the ball and crossed from the right only for Norwood to head over from close range on 21 minutes.
At the other end the closest Charlton came was a Johnnie Jackson header which flashed just wide from a free kick curled in by Stephens.
The second half saw Alnwick deny Smith with a parry at his near post just before Church scored at the other end.
Ward fluffed the chance to equalise by missing an open goal after substitute Sean Scannell pulled the ball back from the byline on 62 minutes.
Town dominated the closing stages but despite half chances and keeper Alex Smithies going up for corners they were unable to find a way through.