The young Blues hosted Bradford City at home in the second round of this season's FA Youth Cup competition with the game played under the floodlights at Brunton Park.
United had a second half first-round fightback against Salford City to look back on for inspiration, with the Bantams having beaten off Rochdale at Valley Parade with a comfortable 3-0 victory.
The game started in the best possible fashion for the young Blues as a free kick, delivered high, caused all kinds of problems. A scramble saw players from both sides try to take charge and it was Charlie Barnes who sparked the celebrations for the home side when he stepped in to poke the ball over the line.
Carlisle went close again when Bell was chopped to the floor at a tight angle just outside the box. Armstrong drilled it low, past the wall, but Donaghy was there to drop low and gather.
Both sides battled hard in midfield as the game tightened up, but Bradford went close when a cross from Staunton flashed across the face of goal. Francis was a whisker away from poking it home.
The Bantams were back on level terms just before the half hour when Kian Scales took matters into his own hands. He had time to set himself as it opened up in front of him and his 28-yard thunderbolt was unstoppable as it whipped into the bottom corner.
The hosts looked to bounce back and fantastic skill from Birch saw him outfox two defenders as he twice dropped a shoulder to get deep inside the area. His cut back found Charters on the move but he had to stretch and he sent his effort an inch over the bar.
It was a good spell of pressure from the hosts, and Lightfoot floated a great delivery to the back stick as Armstrong ran through. The keeper was up high to claim it before the finish could be applied.
Henderson was next to go close when he took a touch from a short Bell pass before letting fly. Donaghy was beaten but it crept past the angle of post and bar.
Back at the Warwick Road End and Robinson came under pressure as he tried to hook a bouncing ball clear as it slowed down on the way into his penalty box. He was off his line, and Morris suddenly had the ball at his feet and a target to hit when the scuffed clearance flew at him. The lob was good, but it had just too much on it and it came to rest on the roof of the nets.
Bradford finished the half strongly and they carved a great opening when Wood sent the ball into the mix. Scales was completely unmarked but he couldn't keep his 14-yard volley down.
Carlisle got forward from the goal kick and Charters opened things up for Bell with a strong challenge and a neat pass. The winger shot from distance but he watched in exasperation as it screwed high and wide.
It took 10 minutes for a very quiet second period to spark into life, and it was United who went close when Bell and Charters worked their way to the edge of the area. Bell looked up and clipped an 18-yard shot past Donaghy, but it screwed the wrong side of the post.
The Bantams took the lead on 57 minutes when Staunton surged forward from his own half with the ball at his feet. His crossfield run brought a through ball to Francis, and he left Robinson with no chance as he crunched a fierce shot off the underside of the bar and over the line.
Carlisle drew level on 65 minutes when a free kick into the box was punched by Donaghy. It fell to Armstrong, 19-yards out, and he kept his eye on the dropping ball before rifling a bullet into the top corner.
It became a midfield war of attrition as the teams cancelled each other out, but Wood had half a sight of the target when he took a short pass from Morris. Day was there quickly to close the shot down.
And United's nets lived a charmed life moments later when a zipped cross from Staunton was met by Francis. The wide man was just five yards out but he somehow guided his header wide.
Donaghy had to dive full length to push a long-range effort from Armstrong away from his bottom corner as the clock ticked down, and a late scramble in the Carlisle box culminated with a wild volley from Morris.
Deep into time added on a mishit corner from the visitors made its way through to Sikora, but the Bradford defender put too much on his header and it edged too high.
Into extra time the teams went, and the Bantams wasted another set piece opportunity when a corner was popped into the side netting by Smethurst.
A shot from DJ Taylor hit a defender and went behind at the other end, but the Bantams surged out in numbers as they protected their goal. Day was caught in two minds in possession for Carlisle and Rowe was suddenly clean through. Robinson stayed big and won the battle of wills as he executed a superb save.
The lively Charlie Wood should have put the visitors ahead for the second time on the night when he found himself with the goal at his mercy and with the ball sitting up nicely. He opted for power and he couldn't believe his bad luck as it screamed over the crossbar.
More danger came from the visitors when Goldthorp put his laces through a shot from distance. Robinson saw it late but he readjusted well to palm it away.
It was a horrible ending to the game for the Cumbrians as a late ball into the box from Goldthorp squirmed its way to Harvey Rowe at the back post. His shot wasn't the cleanest, but it had enough on it to make its way past Robsinson, as he got a touch, and into the bottom corner.
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Goals
Carlisle United - Barnes (3), Armstrong (65)
Bradford City - Scales (26), Francis (57), Rowe (117)
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Bookings
Carlisle United - Barnes (30)
Bradford City -
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Teams
Carlisle United - Robinson, Barnes, Birch, Lightfoot (Taylor 82), Wilson (c), Day, Armstrong, Walton (Swailes 77), Henderson (Soper 65), Charters, Bell (Rooks 111). Subs - Breeze, Steele, Leslie.
Bradford City - Donaghy, Smethurst (c), Staunton, Goldthorp, Sikora, Cousin-Dawson, Francis, Scales (Roberts 110), Morris (Rowe 90), Sukiennicki (Ripley 70), Wood. Subs - Norman, Shanks, White.
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Referee - Mr Alex Beckett
Attendance - 270