Despite being put on the back foot early in the contest, Millwall came close to taking the lead midway through the first half when James Henry rattled the crossbar with a free kick.
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Vaughan could not be deterred though, and he doubled Huddersfield's lead in the 55th minute when he collected a pass from Adam Clayton before drilling the ball past Forde.
Beckford scored his second of the game six minutes later to put the result beyond doubt with a calm finish following good work from Vaughan.
Substitute Jermaine Easter should have snatched a consolation late on but the forward fired over the bar from close range to sum up a miserable afternoon for Millwall.