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The home side were in control early on as David N'Gog dragged his shot wide from a tight angle.
Woods was quickly involved as his powerful strike from distance went just inches wide of the far post.
N'Gog then spurned a glorious opportunity when he scuffed wide from six yards following a fine approach-play from Eagles.
On 60 minutes Bolton capitalised on an error in possession from Huddersfield captain Peter Clarke to break the deadlock.
Clarke was caught out by Marvin Sordell, who quickly found Eagles to smash home the opening goal from close range.
Huddersfield responded brightly as Scannell beat Danny Butterfield before driving just wide of the far post.
The visitors introduced Jermaine Beckford late on, but he could only flick wide in stoppage time as Bolton held on for a crucial victory.