Aldershot substitute Jamie Slabber stunned the 10,803 record breaking Conference crowd by scoring with a header in the fourth minute of injury-time to make the score 2-2 on aggregate.
Two first-half Carlisle goals looked to have settled the tie before Aldershot's dramatic last-gasp effort.
Danny Livesey opened the scoring in the 13th minute, glancing home his fourth goal of the season from a Peter Murphy corner to level the aggregate score.
Chris Billy put United in front after 35 minutes when Brendan McGill left Darren Barnard for dead to whisk in a cross for Billy to sweep home.
Carlisle had chances to add to their score. Glenn Murray came close with a couple of headers and Derek Holmes saw a header hooked off the line by Tarkan Mustafa as early as the fifth minute.
Dwain Clarke and Tim Sills had chances for Aldershot and Steve Watson was unlucky to see his snap-shot rebound to safety off the woodwork in the 52nd minute.
A towering Holmes header came back off the post from a McGill cross two minutes later and David Beharall headed agonisingly over the bar seconds after Slabber's intervention.
Thirty minutes of extra-time failed to produce a goal and the game went into penalties. Will Antwi opened the scoring and Chris Lumsdon equalised for Carlisle before David Lee put Aldershot in front.
Nikki Bull saved from McGill before Slabber made it 3-1 for the visitors and when Murray saw his shot saved, United's chance seemed to have gone.
But Matt Glennon tipped Chris Giles' effort onto the bar and Magno Vieira made it 3-2 before Glennon saved again from Nick Crittenden.
With tension mounting Peter Murphy levelled the scores to send the shootout into sudden death.
Aldershot's Gary Holloway and United's Billy both scored to make it 4-4 and a brilliant Glennon save from Jon Challinor gave the home side the chance to clinch the tie.
Livesey opened the night's scoring and also finished it, giving Bull no chance for Carlisle to shade it 5-4.