Rovers crashed out of the Capital One Cup at the first attempt on a dramatic evening at Brunton Park.
The two sides couldn't be separated after 120 minutes of pulsating cup action, but it was Rovers who lost the resulting penalty shoot 4-3 after the game had ended 3-3.
The home side led at the break thanks to David Amoo's 14th minute opener. The former Liverpool man getting up at the back post to head home John Gilles' centre.
Rovers dominated possession but it took them until the opening moments of the second half to find the back of the net.
They could have had three goals in six minutes as Tom Cairney's deflected effort levelled on 52 minutes, but David Dunn saw a penalty kick saved after Josh King had been felled in the area.
Chris Taylor spared Dunn's blushes as he headed Cairney's corner in at the back post to put Rovers in front on 56 minutes, but the home side wouldn't lie down and levelled thanks to Lewis Guy.
Both sides pressed to avoid the game going to extra-time, Carlisle going closest in added time at the end of the 90 but Mark Beck's header was pushed onto the post by Simon Eastwood.
Extra-time saw Rovers edge in front once more as Alan Judge scored his first Rovers goal with his first touch of the game, the Irishman arriving to volley home after Tom Cairney's free-kick had been cleared.
Unfortunately for Cairney his involvement wouldn't last much longer as the on-loan midfielder received his second yellow card and that gave the home side renewed enthusiasm.
Five minutes from the end of extra-time United drew level once more, David Amoo outpacing the Rovers defence to finish smartly from the edge of the box.
Rovers held an early advantage in the penalty shoot out as Alex Salmon fired over the bar, but missed spot-kicks from Chris Taylor and Josh Morris left substitute David Symington with the responsibility of firing the home side through and he made no mistake from 12 yards.
Boss Gary Bowyer made eight changes from the side that drew with Derby County on the opening day of the season.
Just Alex Marrow, Todd Kane and Josh King retained their places in a starting eleven that saw debuts for Simon Eastwood in goal and Yann Songo'o in defence.
There are also first starts for Chris Taylor and Tom Cairney after their substitute appearances at the weekend.
It was a bright start to match the evening Cumbrian sunshine as both sides looked to gain an advantage early on.
In the 6th minute a cross from Josh Gilles caused consternation in the Rovers box, Gael Givet having to stoop to head away.
At the other end David Dunn tested the Carlisle United back line but his deft lob flew just over the bar.
Two minutes later and Dunn turned provider as his corner from the left was met by the head of Alex Marrow, his effort was blocked and as the ball came out to Josh Morris his sweetly struck effort was deflected away from goal.
Carlisle continued to pose a threat with crosses from the flanks. In the 12th minute a centre from Brad Potts was missed by Gael Givet but fortunately Mark Beck headed straight at Simon Eastwood.
The warning wasn't heeded as home side took the lead on 14 minutes and it was perhaps no surprise that it came from a ball into the box. Josh Gillies with a corner from the left to David Amoo who rose at the back post to head into the corner of the net to delight the home support.
Rovers went straight back up the other end and threatened once more. Tom Cairney's ball was chased into the channels by Josh King, he played it back for Morris to strike but his effort flashed narrowly over the angle.
Despite seeing plenty of possession, Rovers struggled to break down a resolute Carlisle defence, a partially cleared corner was met on the volley by debutant Yann Songo'o but Gillespie got down well to smother.
The visitors would go closer on 36 minutes when from another corner kick Chris Taylor saw his header at the back post skim off the crossbar.
From a Gillies free kick Amoo threatened once more as he again got up at the back of the area, this time he thankfully headed wide of goal.
Rovers enjoyed plenty of possession with neat passing play, but they just lacked that killer ball when it counted as the home side lead at the break.
Ten minutes into the second half and Rovers had turned the game around with a scintillating spell of play.
On 52 minutes Josh King was sent away down the left, and as he reached the area he cut the ball back to Tom Cairney lurking at the edge of the box and his drilled effort deflected off Liam Noble and past the wrong-footed Gillespie.
Two minutes later and Gillespie would be the hero as he saved David Dunn's penalty after Paul Thirlwell had brought down King in the box. The Rovers captain looking for accuracy rather than power but it was a shot that the Carlisle 'keeper read.
However on 56 Rovers would get their second goal after a spell of pressure. Tom Cairney delivering a corner from the right and Chris Taylor got up well to head home at the back post.
But just when it looked like Rovers would up the ante and increase their lead it was the home side who levelled on 62. Good play on the right by Mark Beck saw the forward cross for his strike-partner Lewis Guy and his header crept over the line despite the best efforts from Simon Eastwood.
The two sides continued to exchange changes in an entertaining, end-to-end second half. David Dunn fired over from a Markus Olsson cut back, whilst Mark Beck saw a shot deflect off Songo'o but Simon Eastwood claimed.
A fierce free-kick from Tom Cairney almost beat Gillespie but the United 'keeper did well to push the ball behind, whilst a double effort from Beck saw his first shot blocked and his second held by Eastwood.
With extra-time looming large Rovers pressed for the winner. A quick counter-attack saw Josh Morris find Josh King but he dragged his effort wide, then a defence-splitting pass from Tom Cairney found Morris and he squared for King but his shot was blocked by the chest of a defender.
But Carlisle still had ideas of their own, the lively Mark Beck firing over from the edge of the box.
They then went even closer to grabbing a winner in stoppage time after the 90 as Lewis Guy crossed for Mark Beck. The striker dived low to head goalwards but Simon Eastwood pulled off a sensational save to push the ball onto the post, the ball bouncing agonisingly across the six-yard box and away to safety.
Gary Bowyer made a change at the start of extra-time with Alan Judge coming on for Markus Olsson.
Immediately it paid dividends as the Irishman scored with his very first touch. Tom Cairney's 95th minute free-kick headed only as far as Judge and he volleyed into the back of the net.
To their credit Carlisle showed now signs of throwing in the towel, Mark Beck again testing Eastwood but the Rovers stopper was equal to his effort.
The home side were given renewed enthusiasm when Rovers were then reduced to ten men.
Goalscorer Tom Cairney given his marching orders in controversial circumstances after the on-loan midfielder picked up his second yellow card for a soft challenge on the touchline.
The last 15 were very much a rearguard action from Rovers as Alex Salmon fired wide from the edge of the box before Eastwood saved well from Brad Potts' centre.
Try as they might Rovers couldn't hold on, David Amoo bursting past Todd Kane lash an unstoppable drive from the corner of the area, the ball flying past Eastwood with five minutes of extra-time remaining.
There was still time for Jason Lowe to sting the gloves of Gillespie with a shot from distance before Liam Noble tested Eastwood with a dipping strike.
The two teams couldn't be separated any further which meant penalty kicks were required.
Alan Judge fired home the opening kick but Alex Salmon missed his. Jason Lowe and Jordan Rhodes scored theirs, but leading 3-2 Rovers then missed through Taylor and Morris.
With James Berret and Liam Noble making no mistake from 12 yards it was left to David Symington to clinch the game for the home side and he shot straight down the centre beyond Simon Eastwood.
CARLISLE UNITED: Gillespie, Potts, Livesey, Thirlwell (c), James (sub Brough 43 mins), Amoo, Berrett, Noble, Gillies (sub Symington 89 mins), Beck, Guy (sub Salmon 101 mins).
Subs not used: Fleming, Edwards, Todd, Lynch.
Goals: Amoo 14 mins, 115 mins, Guy 62 mins.
ROVERS: Eastwood, Kane, Songo'o, Givet, Morris, Taylor, Marrow (sub Lowe 46 mins), Cairney, Olsson (sub Judge 91 mins), Dunn (c) (sub Rhodes 93 mins), King
Subs not used: Kean (GK), Best, O'Connor, Fabio Nunes.
Goals: Cairney 52 mins, Taylor 56 mins, Judge 95 mins.
Booked: Lowe, Cairney.
Attendance: 4,372. 891 Rovers fans.