The Terriers went into the game on the back of three matches without a win, which had seen Town move above them, but a goalless first half saw the hosts reduced to 10 men just before the break, Tom Eaves sent off for a second yellow card.
The Tigers should have grabbed a point in injury time, but substitute Allahyar Sayyadmanesh headed wide from six yards out, as the Tigers lost a sixth successive match at the MKM Stadium.
The result saw Huddersfield move on to 66 points, three more than Luton, while they also now trail second-placed Bournemouth by just three points.
However, Carlos Corberan's side have played 40 matches, two more than the Hatters and four more than the Cherries.
Their next encounter is at home to Town on Monday, April 11, who by that time will be level on fixtures played, after hosting Millwall this afternoon and visiting Peterborough on Tuesday night.