United opened up their Central League Cup campaign with an away trip to Poolfoot Farm on Tuesday afternoon.
And they came out on top of a game that could have gone either way thanks to a late strike from substitute Sam Fishburn, who finished from close range following excellent work from Jack Stretton.
Both teams worked hard to close down possession in the opening exchanges but United had half an opening when a huge kick from Breeze found its way to Hardy. He stepped inside to shoot, but it was too close to Donaghy.
Defender Jack Ellis had to be alert at the other end when a deep corner was guided towards Wiredu. He nodded over Breeze, but the captain for the day reacted sharply to clear it off the line.
Connor Teale was perhaps fortunate to only see a yellow when he clashed with Stretton with just 12 minutes on the clock, and it was a feisty exchange that set the tone as challenges and tackles were subsequently exchanged.
A good run from Hardy was met by a neat pass from Hilton as the Blues started to settle into a pattern, but the young forward was disappointed when he blazed over from the edge of the box.
The hosts had a good spell midway through the half and there were appeals for a penalty when Josh Edwards burst through to get onto a pass from Danny Edwards. He shot wide as he tumbled to the floor under pressure from Maddison. The officials showed no interest.
Strength from Will Russ saw him turn smartly when he controlled with his back to goal, and his shot was angling for the bottom corner until Breeze dived long to make a fantastic save.
And the big stopper was in action again moments later when White went for glory from distance. Quick feet allowed a comfortable save to be made.
It was suddenly all about Carlisle and Charters strode forward before sliding a neat pass onwards for Stretton to chase. The forward got there as Donaghy bore down, and he was an inch away with a clipped effort that bounced the wrong side of the upright.
United got forward in numbers on the stroke of half time and Stretton beat the offside trap to come at the target from a tight angle. Donaghy spread himself to block, but it was quickly recycled to the back stick. Nugent was left with his head in his hands as his volley struck Johnston and spun away to safety.
There was more work for Gabe Breeze after the break, and he was at his best to deny Russ when a stinger whipped towards the bottom corner.
He was then at full length to first parry and then smother a thumping header from Devlin that was set to bulge the nets.
The Cumbrians rallied and they worked the ball well, with Nugent and Carr instrumental in finding a way through. The delivery from Nugent was met by a glanced header from Bollado, but he was thwarted by a combination of the keeper's fingertips and the woodwork.
Hilton rattled a 28-yard free kick wide and high as half chances came and went for both teams, and Donaghy had to parry a fierce strike from Hilton when he cut in from the right flank with the ball at his feet.
It was still very much in the balance, and Dan Edwards showed real frustration as he danced through two challenges only to thrash the ball into the bushes when he had just the keeper left to beat.
Carr blocked McMillan as he threatened to find a finish, but the pass of the day from Sonny Hilton had the Blues back on the front foot when he looked up from deep inside his own half.
He stroked the ball with the outside of his right boot, and that sent Stretton free and clear when he picked it up 40-yards later. Donaghy showed great anticipation to prevent the goal.
Josh Edwards and Danny Edwards were met by a wall of resilience from the excellent Gabe Breeze, and his double save provided a springboard for the game to be won.
Substitute Sam Hetherington threaded an inch-perfect ball down the line to Stretton, and he bullied his way into the box. His low cross had fizz and power, and Sam Fishburn said ‘ta very much’ as he slotted it home from just four yards out.
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Goals
Carlisle United - Fishburn (90)
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Bookings
Fleetwood Town - Teale (12), Wiredu (57), Johnston (77)
Carlisle United - Stretton (87)
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Teams
Fleetwood Town - Donaghy, Johnston, Devlin (Bird 67), Teale, J Edwards, Wiredu, Boyle, White, D Edwards, McMillan, Russ. Subs - Cairns (gk), Raffie, Brown, Johnson.
Carlisle United - Breeze, Maddison (Hetherington 78), Ellis (c), Idehen, Charters (Hill 74), Nugent (Fishburn 53), Carr, Hilton, Bollado, Stretton, Hardy (M Bell 53). Subs - Kelly (gk).