Goodwin, who joined Town on a free transfer from Scunthorpe in the summer, rose highest to nod home Gary Roberts' corner after 65 minutes.
As Scunthorpe pushed for an equaliser late on, Roberts sealed the win after tapping home into an unguarded net.
The visitors rattled the crossbar via a rasping left-foot drive from distance from Sam Togwell after 19 minutes.
After the break, Huddersfield's Keigan Parker latched on to Roberts' pass only to fire straight at Scunthorpe's Joe Murphy when well placed.
Scunthorpe searched for a leveller in the dying minutes, with Gary Hooper shooting straight at Alex Smithies, before Roberts clinched victory with the last kick of the game.