Huddersfield Town 0 Carlisle United 2
Garner, 19, moved to Brunton Park in the summer for £140,000 and his header a minute from the break sealed a third straight win for caretaker boss Greg Abbott.
However, the man of the match was another summer signing Marc Bridge-Wilkinson, who ran the midfield.
Bridge-Wilkinson had a hand in both goals and was unlucky not to have scored himself.
Huddersfield, on the back of two successive victories, were missing four key players and it showed.
Luke Beckett had a glancing header go wide for the home side before Chris Brandon fired into the side netting.
Carlisle's Danny Graham had a goal disallowed before his side took the lead in the 34th minute.
The Terriers defence were all at sea as Bridge-Wilkinson and Graham were denied by former Cumbrians keeper Matt Glennon. Still Town could not get the ball clear and Bridge-Wilkinson had another shot tipped on to the post by Glennon.
The ball finally dropped for defender Danny Livesey who slotted home from close range.
A minute from half-time Carlisle sealed the points. Bridge-Wilkinson's pinpoint corner was met by Garner, who beat three flat-footed Town defenders to power a header past Glennon.
After the break Bridge-Wilkinson forced Glennon into two more saves as Town laboured with strikers Beckett and Malvin Kamara starved of service and unable to conjure up much of a threat.