Bradford City 0 Huddersfield Town 1
But Town may find themselves in trouble after objects were thrown at City defender Nathan Doyle after he was involved in the sending-off of full-back Danny Adams.
The Bantams, who could have moved into the second automatic promotion spot with a win, were frustrated by Town's 4-1-4-1 formation and Hudson, who scored in Huddersfield's win in the corresponding fixture last season, made the most of some sloppy defending to put the visitors ahead.
Huddersfield manager Peter Jackson set out his stall to stifle Bradford's attacking play and his side's early work-rate paid dividends as City struggled to create any real clear-cut chances.
After nine minutes, Town goalkeeper Matt Glennon tipped away a long-range strike from City's young winger Joe Colbeck, but it was a rare opportunity.
Home custodian Donovan Ricketts then had a lucky escape after he failed to reach a Michael Collins corner and Martin McIntosh saw his header booted clear.
The division's joint leading scorer Gary Taylor-Fletcher turned provider for Town after 25 minutes when City's defence was caught out by a quickly-taken throw-in.
The Terriers hot-shot had too much time to deliver a perfect cross from the right and Hudson, who is 26 later this month, headed home unchallenged from eight yards out.
City struggled to make an impact in the closing minutes of the half, but their leading marksman Dean Windass wasted two good chances.
The 37-year-old frontman fired a volley high and wide two minutes before the break and then, in injury time, he beat the Town offside trap only to drag a poor shot wide of the target.
Bradford winger Lee Holmes saw his cross-shot fly inches wide of the far post in City's first attack after the break, but the Bantams still lacked that killer touch in front of goal.
After 72 minutes Adams was given his marching orders for a late challenge on Doyle to boost City's hopes - but Town keeper Glennon pulled off two crucial saves.
In the closing stages he pushed out Eddie Johnson's near-post header and, deep into injury-time, he did well to block a Windass strike.