Town have beaten their West Yorkshire neighbours in three successive matches and cast doubt over the visitor's promotion aspirations.
Centre-back Clarke claimed his third goal of the season and local bragging rights, when he rose unmarked to head home the only goal.
Clarke pounced between skipper Richard Naylor and Andrew Hughes to power past Casper Ankergren.
Leeds badly missed 23-goal top scorer Jermaine Beckford, banned for three matches by the FA for an elbow in the victory over Millwall on Monday.
Strikers Lee Trundle and Luciano Becchio were starved of service but Leeds had enough chances to take a point from the game.
Town's highly rated teenage keeper Alex Smithies turned in an impressive display to keep a clean sheet and protect an unbeaten home record under new boss Lee Clark.
Smithies made his first crucial save from the dangerous Robert Snodgrass just a minute before Gary Roberts launched the 16th minute corner for Clarke to score.
Both sides played some smart passing football in the first half and Andy Robinson's shot was beaten out by Smithies.
Snodgrass sent over a corner and Smithies was there again to save from Manuel Rui Marques.
Young striker Lukas Jutkiewicz, making his Town debut on loan from Everton, saw a shot deflected over by Rui Marques and Anthony Pilkington lost his marker but was off target with his header.
Leeds were the better side after the break but battling Huddersfield and Smithies prevented an equaliser.
Substitute Jonny Howson nodded wide before Smithies blocked Robinson's header and kept out a side footed effort from Snodgrass.
Leeds almost levelled two minutes from time, but Naylor's header struck a post.
Huddersfield could have sealed it in stoppage time when Michael Collins was clean through on goal, but Ankergren grabbed the ball off his toes.