The Cumbrians looked in control at 2-1 up with just five minutes to spare but last-gasp goals from Padraig Amond and Andrew Procter sealed a second round date with Tranmere Rovers.
Their cause certainly wasn’t helped by the dismissals of Peter Murphy and James Berrett as they eventually succumbed to Stanley’s superior numbers.
There was more drama in the Southern Section at Leyton Orient’s Brisbane Road as visitors Dagenham & Redbridge emerged triumphant thanks to an extraordinary 14-13 shootout victory.
A staggering run of 27 successfully converted penalties was brought to an end when Ben Chorley saw his effort saved by goalkeeper James Shea.
The Daggers looked set for victory in normal time when Sam Williams struck in the 64th minute but a leveller two minutes from time from David Mooney forced the spot-kick lottery.
Elsewhere League One side Wycombe Wanderers sealed their passage into the second round as a Stuart Beavon hat-trick secured a 3-1 win over Bristol Rovers.
Former Chairboy Matt Harrold also got his name on the score-sheet but his 58th minute effort was in vain as Beavon left with the match ball and a second round home clash with Cheltenham Town in the bag.