Clarke rose unmarked to nod home Gary Roberts' corner after 16 minutes of a hard-fought League One clash.
The visitors had chances of their own in the first half, but Huddersfield goalkeeper Alex Smithies was on hand to keep out efforts from Robert Snodgrass, Andy Robinson and Rui Marques.
At the other end, home debutant Lucas Jutkiewicz tested Casper Ankergren, while Anthony Pilkington headed a Roberts cross inches over the bar.
Leeds had the better of it in the second period, as Snodgrass' drive was well saved by Smithies and three minutes before the end Whites skipper Richard Naylor hit the post with a header as the visitors looked to salvage a point.
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