Chris Maguire’s first goal for the Imps was not enough to send his side through to the third round of the Papa John’s Trophy.
Michael Appleton made five changes to the side which started Saturday’s Sky Bet League One visit of Accrington Stanley.
The Imps started brightly, with Hakeeb Adelakun and Dan Nlundulu - both brought back into the starting XI - combining in the first minute to fashion an opportunity for the latter which went narrowly wide.
They enjoyed plenty of early success down the right, with Adelakun twisting and turning before a powerful drive which Mark Howard stopped with his legs.
That started a run of four successive corners for the Imps, from which the ball was worked back to Lewis Fiorini, whose cross was headed behind for another set-piece.
The best chance from the run of corners was a shot from Max Sanders which Howard did well to turn behind.
It took nearly a quarter of an hour for the home side to threaten, and even then Jon Mellish’s low shot was tame and did not test Josh Griffiths.
A central free-kick just outside the area moments later provided the Cumbrians a second opportunity, but Zach Clough’s shot was straight at Griffiths who held comfortably.
The Imps continued to enjoy the majority of possession, with Adelakun and Regan Poole combining effectively down the right.
One move down the right led to the ball being played inside to Fiorini, whose powerful effort went just over the bar, while Sanders also saw an effort blocked.
Carlisle threatened on the counter after half an hour, winning a corner from which Rod McDonald had an effort deflected onto the woodwork.
But the good movement from the Imps continued, and by the break eight corners had been won. It took until the verge of half-time for the deserved breakthrough to come, and it was no surprise it followed a smart move down the right.
It started with yet another mazy run from Adelakun from the right. He played a one-two with McGrandles, before laying the ball off to Maguire who smashed the ball home.
The rain came pouring down during the interval and the early period of the second half, creating difficulties for both sides.
The home side were gifted an opportunity to draw level after 53 minutes when Jordan Gibson latched onto a loose ball and rounded Griffiths, only for his effort to finish up - from his perspective - on the wrong side of the post.
It was the Imps who continued to create the most opportunities, though, with a Sanders shot deflected wide.
It took a brilliant fingertip save from Howard to deny Adelakun after the forward picked the pocket of Brad Young as the home side failed to cleat the corner won by Sanders - with his powerful drive being tipped onto the near post by Howard.
The Imps were dominant now, but the home side drew level with a defence-splitting pass from Manasse Mampala finding the run of Jack Armer who finished smartly into the bottom-right corner.
Free-flowing football was hard to produce in the wet conditions, but the Imps set about trying to find a winning goal.
Adelakun put in a dangerous cross from the right which was cleared, while it took a vital defensive header from the goalscorer Armer to stop a Maguire cross finding McGrandles six-yards out with the goal gaping.
When a low Fiorini effort drifted just wide after 82 minutes you began to get the feeling it was not going to be the Imps’ night.
And so it proved as it went to penalties, with Maguire and Montsma missing as the Cumbrians progressed 4-3.
Attendance: 884 (75 away)