The Cumbrians have slipped into relegation trouble but on this form they will quickly move up the table.
Danny Graham gave them an early lead then second-half goals from Michael Bridges and Graham Kavanagh sealed Huddersfield's fate leaving new boss Lee Clark to reflect on his first defeat in charge.
Carlisle, without a win in the previous four games, gave a sparkling first-half performance and took a 12th-minute lead when Bridges played the ball in low towards the near post and Graham reacted quickest, nipping in front of keeper Alex Smithies to turn the ball home from a couple of yards out for his 13th goal of the season.
However Bridges added to the scoring in the 55th minute, sliding a 12-yard shot past Smithies for Carlisle's second goal after his own initial pass had come back to him off Graham.
Carlisle's third goal came in the 75th minute when veteran midfield man Kavanagh played the ball forward to Graham and ran onto the striker's chested lay-off to fizz a low 20-yard right-footer past Smithies.