United went into the second of their Leasing.com group fixtures knowing that they needed to win to give themselves a chance of progressing to the knock-out stages.
Blackpool came to Brunton Park with a healthy victory over fellow seasiders Morecambe under their belts and with the knowledge that a victory would see them safely through the first phase.
Boss Steven Pressley made nine changes from the Saturday starting line-up as he looked to his fringe players to put a knock on his door for a league start.
The Blues won an early corner and an inswinging delivery to the back post was nodded wide by Hayden as he battled to make space for the header.
Blackpool responded in kind when a cross from MacDonald was put behind by Elliott, and the home side cleaned up when the set piece delivery came in.
Keeper Louis Gray was needed when Delfouneso tried his luck from 25-yards, having played a one-two with Hardie to create an opening, and the keeper was equal to it as he got his body behind the ball.
The Tangerines stayed forward and Spearing blazed a long range effort over the bar when a gap opened up in front of him. He had runners left and right but he opted to go for the drive.
It was almost put on a plate for Stefan Scougall on the quarter hour when a kick out from Mafoumbi fell short of Edwards. The midfielder raced in and nicked the ball but his touch was heavy and that took it behind to safety.
Disaster struck for the hosts midway through the half when McKirdy stayed on the floor after a meaty challenge in the midfield area. He limped off to be replaced by Jack Bridge.
United pressed well just after the switch and a hurried clearance from Anderson, as he came under pressure from blue shirts, spun out of the air to be controlled by Bridge. He skipped past his man and pulled the ball back but the away side recovered to go on the break.
Determination from Guy brought a corner at the other end, and Gray initially did well to deal with a thumping header from Nottingham. MacDonald was on to the loose pieces and his low, fierce grasscutter of a near post cross appeared to have been gathered by the Carlisle stopper, but it somehow found its way over the line.
Blackpool grew in confidence after the goal and a passing move left Shaw in a dangerous area as he looked up to find his cross. Guy showed for it as he made a near post run but his volley went well wide.
Better came from the Blues as they moved the ball quickly through midfield with Scougall, Carroll and Bridge at the heart of it. Elliott overlapped but Mafoumbi was off his line quickly to gather the twisting curler in.
And they spurned an excellent opportunity to get back on terms when they broke from deep, with Bridge in possession. He slid it through to Loft and he did well to leave his marker in his wake as he bore down on goal. He looked to draw the keeper but he miscued his chip and it bobbled and twisted its way past the upright.
Gray was down smartly to handle a 19-yarder from Hardie as half time approached, but it was United who were celebrating in time added on for the period when Ryan Loft was played clean through from deep. He held his man off and made amends for his earlier miss with a neat touch which spooned up off the keeper and into the back of the net.
Both sides tried to press at the start of the second half, with moves breaking down in the penalty areas, and there was a superb ball from Iredale which begged to be put away as he dropped a shoulder, beat his man and whipped it in. It was touched behind for a corner, but that came to nothing as the Seasiders cleared their lines.
Carlisle tails were up and Scougall arrived late to get on the end of a good flowing move, with another teasing cut back to follow. Anderton did well to get a leg in the way before Sorensen could shoot.
Another late challenge left Bridge writhing in agony on the floor and it was immediately apparent that he was in pain. A stretcher was called for but he gingerly got to his feet and limped to the sidelines. He came back onto the field of play, following his treatment, but he struggled to shake it off and was quickly replaced by Mo Sagaf.
Nathan Thomas forced a two-handed save out of Mafoumbi when he sent a 28-yard free kick over the wall. It dipped late and was threatening to creep under the bar until the stopper intervened.
Blackpool were gifted a chance with just over 10 minutes left to play when a loose pass in midfield put Bange clean through with just Gray to beat. The big striker tried to slide it into the bottom corner but the stopper was equal to the task as he got down low to make a vital save.
Gnanduillet then got on the end of a cross from Turton in what was a good spell for the away side, but Gray was once again well positioned to grasp it out of the air.
The Cumbrians then went close as Thomas used pace to burst down the right flank, and he did well to take the defender out of the equation before curling it beyond Mafoumbi. The keeper looked on in relief as it crashed back off the upright.
Hayden sent a corner from Sagaf wide when he jumped highest to meet it with a header, but it was Carroll who won the tie for the hosts with a stunning shot from 30-yards which swirled its way beyond Mafoumbi as he flapped his hands at thin air.
Carlisle United - Loft (45), Carroll (87)
Blackpool - MacDonald (25)
Carlisle United - Mellish (38), Carroll (69)
Blackpool - Spearing (74)
Carlisle United - Gray (gk), Branthwaite, Hayden, Mellish, Elliott, Scougall (c), Carroll, McKirdy (Bridge 21 (Sagaf 65), Iredale, Sorensen, Loft (Thomas 66). Subs - Robinson (gk), Charters, Kerr, Birch.
Blackpool - Mafoumbi (gk), Anderton, Edwards, Delfouneso (Turton 58), Spearing (c), Hardie (Gnanduillet 53), Nottingham, Scannell, Guy, MacDonald, Shaw (Bange 72). Subs - Howard, Heneghan, Tilt, Husband.
Referee - Darren Handley
Assistant Referee 1 - Billy Smallwood
Assistant Referee 2 - Simon Clayton
Fourth Official - Nathanael Cox
Attendance - 911 (216 away fans)