Newport County extended their winning run to five games to maintain their promotion challenge in the Blue Square Bet Premier.
Christian Jolley broke the deadlock early on and the visitors held out.
The striker latched on to a clearance from 25 yards out and lofted his effort over home goalkeeper David Carnell.
Victory allowed Justin Edinburgh's side to close the gap on leaders Wrexham to three points while Hyde are now one point above the relegation battle.
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Newport County manager Justin Edinburgh told BBC Radio Wales: "Delighted with the result.
"Scrappy game, but it took a little bit of magic from Christian Jolley to secure the three points for us.
"He's always got that composed finish. Him and Danny Crow are striking up a very good partnership.
"I'm pleased with the goal, but the most important thing for me was a clean sheet.
"We haven't won many scrappy games like that this season so it's nice to see us do that at a crucial time in the season."