The Cumbrians shocked The Terriers with Peter Duffield tapping home from close-range after 72 minutes for a crucial winner.
Carlisle are still bottom despite the win however they are now just nine points behind Rochdale, who drew 1-1 at Swansea.
Rochdale had looked set for the win following Leo Bertos's 26th minute opener, however Bradley Maylett earned a share of the spoils late on.
Elsewhere, Darlington eased their relegation pressure with a 2-1 victory over Cheltenham at the Reynolds Arena.
Goals from David McGurk and Barry Colon put the home side two-up only for Grant McCann to pull one back, but it proved nothing more than a consolation.
York's poor run of form continued following a 3-1 defeat to 10-man Scunthorpe at Bootham Crescent.
Former Grimsby player/manager Paul Groves opened the scoring after 17 minutes and their lead was doubled from the spot by Steven MacLean after 16 minutes later.
Substitute Jamie McCombe saw red for picking up two swift yellow cards shortly after half-time despite only coming on at the break.
The loss of a McCombe failed to slow down the visitors with Groves adding his second, however Andy Bell did give the home supporters something to cheer with a late consolation.
See below for match summaries:
Carlisle 1-0 Huddersfield
Darlington 2-1 Cheltenham
Swansea 1-1 Rochdale
York 1-3 Scunthorpe
Click here for the latest Third Division table.
