Jackson Irvine’s goal left Town needing to beat Norwich at home on Wednesday to maintain slender hopes of automatic promotion.
Town coach David Wagner had made five changes from the side that lost 4-0 at Bristol City before the international break with Whitehead coming in in place of neck injury victim Jonathan Hogg, partnering Aaron Mooy in the centre of midfield.
Mooy had returned early from international duty with Australia after being suspended for Tuesday’s World Cup qualifier against the UAE, a game in which Irvine scored. His late return meant only a place on the bench against Town.
Michael Hefele replaced Mark Hudson in the centre of the Town defence and, with Izzy Brown injured and Elias Kachunga and Nahki Wells rested to the bench, Joe Lolley, Jack Payne and Collin Quaner were given attacking duties.
Ben Turner, facing a five-match ban unless an appeal against a racial abuse verdict is successful, made some important blocks for Burton in the early stages during which Lolley went close with a curling effort.
Tommy Smith went down in the area on the overlap but failed to win a penalty and Jon McLaughlin did well to beat away a shot from Payne for a corner.
Tom Flanagan, whose challenge on smith went unpunished, had a penalty claim of his own denied when challenged by Chris Lowe.
Whitehead went in the book for a late challenge on Michael Kightly but Hefele escaped for an off-the-ball challenge which left Kyle McFadzean on the ground clutching his face.
Burton’s stalling tactics did not go down well with the home fans but it was goalless at the break.
Marvin Sordell could have given Burton the lead in the 51st minute when he easily cut inside Hefele but his low shot lacked power to trouble Danny Ward.
Town made a double substitution in the 55th minute with Wells and Kachunga replacing Payne and Lolley and Irvine entered the fray eight minutes later for Kightly.
Wells went tumbling under John Mousinho’s challenge but again play was waved on.
A fierce effort from Lowe was beaten away by McLaughlin at full stretch as Town pressure built Mooy being blocked eight yards out and Quaner fluffing the follow-up chance.
Burton had used all their substitutions by the time Philip Billing replaced Quanner in the 79th minute.
The Brewers went close when the ball fell for Flanagan from a cross from Lucas Akins but Ward blocked the drive with his legs.
Town forced two corners in succession and Whitehead got his marching orders for a second yellow for an alleged elbow after Hefele’s header had been headed off the line by Brayford.
Burton forced two late opportunities and they broke two on one with Sordell breaking through the tackle of Lowe before drawing Ward and setting up a simple tap-in winner for the Socceroo.
Huddersfield: Ward, Smith, Hefele, Schindler, Lowe, Whitehead, Mooy, Lolley, Payne, van La Parra, Quaner. Subs: Hudson, Billing, Kachunga, Holmes-Dennis, Coleman, Cranie, Wells.
Burton Albion: McLaughlin, Brayford, Mousinho, McFadzean, Turner, Flanagan, Christensen, Murphy, Kightly, Woodrow, Sordell. Subs: Akins, Dyer, Bywater, McCrory, Naylor, Varney,
Referee: Scott Duncan (Tyne & Wear)