Skipper Frank Simek converted the winning penalty as Carlisle completed a fine fightback to knock Port Vale out of the Johnstone's Paint Trophy after the game finished 2-2 after 90 minutes.
Carlisle, last season`s beaten finalists, appeared to be heading out of the competition at the second-round stage as they trailed 2-0 with 14 minutes left but they hit back to keep alive their hopes of another date at Wembley.
Vale took the lead in fortuitous circumstances three minutes before half-time. There appeared to be little danger from Louis Dodds' ball in from the right until Oliver Norwood, in trying to clear, succeeded only in sending a header arrowing into the bottom corner.
With Carlisle struggling to string their passes together Vale doubled their lead in the 64th minute when Marc Richards met Rob Taylor's cross six yards out and his downwards header carried sufficient pace to slip from Adam Collin's grasp and bounce behind the keeper over the line.
Carlisle's first goal in four home games finally came in the 76th minute when James Chester met James Berrett's free-kick from the left to thump a header past Chris Martin from 10 yards.
Five minutes later the home side were level when Jason Price, one of three second-half substitutes, got on the end of Kevan Hurst's cross from the right and steered a first-time shot past Martin from close range. Collin then saved from Tommy Fraser and Dodds in the shoot-out, leaving Simek to fire home the decisive kick.