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Orient were woeful in the final third of the pitch throughout the first half and did not muster a shot until the 45th minute when Jason Demetriou fired just wide.
Huddersfield midfielder Malvin Kamara had earlier twice laid on chances for Phil Jevons but the striker wasted both.
At the start of the second half, Demetriou forced Town goalkeeper Matt Glennon to make his first save of the match and, with 13 minutes left, Beckett struck the winner after good work from Andy Booth and Andy Holdsworth and the Terriers held on for victory.
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