Carlisle scored four goals without reply to leave Huddersfield rocking and give themselves a great chance of a return visit to Wembley when the sides meet again in the second leg of the Johnstone's Paint Trophy in three weeks' time.
First-half goals from Ben Marshall and Tom Taiwo were no more than Carlisle deserved for some flowing football. The Cumbrians added to their lead with headers from defenders Peter Murphy and Lubo Michalik midway through the second period.
Apart from a late header by Jordan Rhodes which flew narrowly past the post, Huddersfield never looked like a side that had won their last four games.
Carlisle took the lead in the 19th minute with a neatly-worked goal. Francois Zoko turned Craig Curran's ball into the path of Marshall who burst into the box at pace before slipping his shot past the advancing Ian Bennett.
Carlisle's purple patch continued in the 23rd minute when Taiwo slammed home a right-foot shot from the edge of the box after brilliant skill by Zoko on the left had split the Huddersfield defence apart. The Cumbrians were unlucky not to go further in front in the 58th minute when Michalik's close-range shot was cleared off the line by Antony Kay.
But within four minutes Murphy had come up from the back to thump home a header from James Berrett's right-wing corner. And in the 65th minute it was 4-0, this time Michalik charging in at the near post to nod Berrett's pinpoint free-kick past a startled Bennett.