United faced Cleator Moor Celtic on Wednesday night in the quarter-final of this season's Cumberland Cup competition.
The Blues had their under-18 side out for the game, with Nic Bollado and Mason Hardy leading the line behind a diamond-shaped midfield.
Celtic had the first attack of the night as Maguire showed strength to keep possession. It eventually came to Hall, but his effort from the edge of the box was charged down.
A free kick from the right wing from Mahone caused problems as it dropped in the six-yard box. Breeze was off his line to punch, and he got good distance on his clearance.
The Hoops kept coming and a neat exchange between Birdsall and Ward saw a backheel almost release the latter. Kilsby stuck out a boot to stop the move.
United showed when Kai Nugent went with pace and power through the midfield. He bounced the ball off Garvey, and it eventually spun free for Hardy to strike. His volley was on target but it was easy for Rule to gather.
A measured pass from Garvey sparked another good move as Hardy ran with the ball at his feet. He tumbled, under the close attentions of Tatton, and the match official surprised everyone when he produced a red card to send the Celtic man from the pitch.
The hosts rallied despite the numerical setback and a flighted free kick from Ward was met by Birdsall, who nodded the ball into the deck. There was an almighty scramble, with a queue of players trying to stab it home, but Breeze and his back line stood strong to see the moment through.
Breeze was in action again when Wetherall beat his man to aim a pass at the front stick. Birdsall got a toe to it but the stopper spread himself to make a vital block.
There was another let off for Carlisle when Birdsall hooked a deep ball back across the face of goal. Kilsby had dropped behind his keeper and he stepped in to make the clearance.
Rule showed safe gloves at the other end when Bollado twisted away from his marker to feed it to Watt. A stinging drive from distance was pulled into the chest.
The half closed with a whisked 22-yard free kick from Watt which arrowed past the wall. Rule was attentive and he put two fists to it to beat it away.
And Bollado beat the offside trap as the ball was recycled to go one-on-one with Rule, but the angle was tight and the keeper made the save. The corner was drilled and the big striker was disappointed when he glanced his header just over the target.
A flick from Birdsall from a long kick forward released Wetherall at the start of the second period but the punt from distance sailed high and wide.
And there was a real chance for Wetherall just seconds later when Maguire lofted the ball high over his shoulder and into the mix. The wide man had a free header, just ten yards out, but he somehow guided it wide.
Birdsall was next to go close when he shielded a throw from Mahone with his back to goal. He stayed tight to his man and wasn't too far away as he rattled a crisp volley just past the upright.
Celtic kept pushing and a neat touch from Birdsall from a Ward delivery left Maguire with half a sight. He connected cleanly and Breeze had to watch it all the way.
Another Maguire curler had to be captured by Breeze as Birdsall and Ward once again did the legwork to open the door, and Wetherall teased one into the advertising boards as the home side continued to ask the questions.
The hosts wasted another gilt-edged opportunity when a pinpoint free kick was met by Glover. He was unmarked, at very close range, but it came off his shoulder and spooned over the target.
Missed home opportunities were punished on 79 minutes when Watt flicked a clever ball into the box. Bollado forced a save out of Rule, but Hardy was onto the rebound in a flash. He made no mistake as he bulged the net.
Bollado was the width of the ball away from sealing the deal on 88 minutes when he shot low after a Carr attempt had deflected his way. It struck a defender's heel and bobbled to safety.
Mahone levelled things up for the ten men in time added on with a stunning strike as the away side failed to deal with a high bouncing ball. The volley was a rasper and Breeze could do nothing.
Bollado rattled the post in the first period of extra time when he let one go from the edge of the box, and Romeo Park sent one just wide when he tried the same.
But the lead was regained in style when Bollado spanked a beauty from distance past the keeper with 104 minutes on the clock.
Maguire had a low shot that flew through legs at the start of the second spell, and Watt and Park had efforts closed down when the pair led a charge on the counter.
Celtic had another clear-cut opportunity late in the day when Celtic won a header from a dipping free kick. Mahone had ghosted in, completely unmarked, but he got his touch wrong and his frustration shone through as he realised that a big moment had passed.
DJ Taylor beat the offside trap to send Watt into a good area, but he blazed it high when he pulled the trigger. The same player struck the inside of the post in the next attack, after Park had slid the ball his way, and the whistle blew on what had been a keenly fought encounter with United having booked their place in the semi-finals - but not before the home side were reduced to nine men when Wetherall was dismissed.
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Goals
Cleator Moor Celtic - Mahone (90)
Carlisle United - Hardy (79), Bollado (104)
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Bookings
Cleator Moor Celtic - Smith (20), Mahone (45), D Little (90), Charlton (117), Glover (120)
Martin Mahone (manager - 41)
Sent off - Tatton (20), Wetherall (120)
Carlisle United - Bell (90)
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Teams
Cleator Moor Celtic - Rule, Mahone (c), Smith, J Little, Tatton, Close (Charlton 105), Ward (D Little 86 (Johnston 114)), Maguire, Birdsall, Hall (Glover 21), Wetherall. Subs - Jackman.
Carlisle United - Breeze, Gordon (Hill 70), Barnett, Kilsby (c), Bell, Carr, Nugent (Taylor 65), Watt, Garvey, Hardy (Park 85), Bollado. Subs - Simons (gk), Swinburn.
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Referee - Scott Henry
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Attendance - tbc