A fantastic team display from Carlisle United took them into extra time and then onto penalties against Premier League giants Liverpool, but a string of spot kick saves from Bogdan eventually took the Reds through.
The hosts came flying out of the blocks and a shot from Firmino had to be dealt with by Gillespie as it skipped up off the slick surface. Lallana was just wide with a long range effort as the red shirts stayed forward and Firmono drilled another decent attempt just past the upright as the home chances rained in.
A cross from Can caused problems as Lallana arrived late in the box but Gillespie was off his line quickly to push the loose ball away. Joe Allen was next to try his luck with another poke from distance and Raynes had to react quickly as a stinger from Ings was parried back into the mix by firm hands from the keeper. The defender did enough to force Lallana to nod his follow up into the stands.
Carlisle started to settle and a surging run from Hery from out of his own half took him to the edge of the box. He hit it on the run and it dipped just over the target.
A great build up from the Blues, which involved Hery, McQueen, Asamoah and Dicker, brought a superb far post delivery from Grainger, but McQueen couldn't quite get there as it dropped beyond the far post.
Liverpool reasserted some authority as Ings and Lallana kept the long range efforts coming and they grabbed the lead when Lallana was allowed to overlap unattended on the attacking left flank. A lovely cross invited Danny Ings to thunder his header in from close range.
The pace of the game subsided following the goal but Ings went close again when Moreno floated a pinpoint cross onto the penalty spot. The big striker directed a precise header past the dive of the keeper but also just past the post.
United were down, but not out, and a slide rule pass from midfield sent McQueen past his man and onto the byline. His cut back fizzed across the face of goal but Asamoah couldn't make up the ground.
Liverpool looked dangerous on the break and Ings ripped a rasper over the angle of post and bar as he continued to look the most likely to score.
But the Cumbrians stunned the Kop into silence when the dangerous Bastien Hery went right at the heart of the defence following an intelligent pass from Joyce. He spotted Asamoah in space and the front man didn't disappoint as he took a touch before drilling the equaliser into the bottom corner.
The Reds preferred to shoot from distance and both Can and Allen sent efforts right at Gillespie as the home fans became restless as the half time whistle approached.
Half chances were the order of the day early in the second half and a toe poke from Milner was comfortable for Gillespie as home shirts flooded the box. The keeper received more of a test when Origi dropped his shoulder and made space. The shot angled for the corner until the stopper went long to beat it away with both hands.
An intricate exchange of headers inside the United area from Lallana and Ings left Origi with another clear sight. He went for a first time volley but he lost his bearings and sent it at the corner flag.
A deflected punt from Can brought another corner but the delivery from that was too high for Skrtl. He got to it but he could do little to keep it on target.
Origi saw more of the ball but another header on the rise from a Milner cross was easy for Gillespie to claim. The stopper earned his corn from the next attack as Lovren sat deep to pick up the half clearance. His shot had purpose and it needed another excellent one-handed save to keep it out.
That man Origi rattled another wayward shot into the Kop as home anxiety levels grew and the introduction of Coutinho as a substitute almost had an immediate impact as he played a one-two with Milner. His shot was top corner bound until Raynes got a vital touch.
The confident Mark Gillespie plucked another Lallana shot out of the air as he was forced to go again from distance and another good save, this time from Coutinho, kept the scores at level pegging.
Newcastle youngster Macaulay Gillesphey marked his debut appearance with a touch on a Milner shot which took it into the side netting, and Lallana was wasteful when he found himself unmarked at the back stick. It fell nicely but he couldn't keep his volley on target.
An excellent cross from McQueen had to be defended at the other end as Gillesphey threatened with a finishing touch and the corner from Grainger had Ibehre and Raynes interested, but neither could quite make it count.
A late Coutinho effort skimmed the outside of the post and the same player sent another wild curler into touch as the clock ticked down and extra time beckoned.
Early blocks from Coutinho and Origi continued the theme of the night in the first half of extra time and Carlisle almost nabbed the lead when Joyce and Hery combined to put Ibehre through. He took it early and Bogdan was well placed to pull it into his chest.
The visiting goal lived a charmed life on 100 minutes when it came loose for Milner to hit. Gilliead's touch took it onto Gilliespie and Origi's effort on the spin was deflected over by lunges from Gilliead and Raynes.
United gave as good as they got as they attacked on the break but they had another scare when Lovren wriggled free at a corner. His header was strong but always off target. The same player brought another save when he was forced to shoot from deep again by the stubborn defence, and Ings was next to be wasteful when he blazed over as he latched onto a ball over the top.
Milner dragged a poor shot wide and Can put another one over as the Reds found their route to the 18-yard box continually cut off, but Gillespie had to be brave again as he raced out to shorten the angles as Lallana ran clear.
Liverpool were reduced to ten men when Lovren was stretchered from the field and there was almost a sting in the tail when Gilliead tried his luck. He caught it well but it spun just past the angle of post and bar.
Milner - low to the keeper's right - 1-0
Grainger - low to the right, saved by Bogdan - 1-0
Can - cheeky top corner chip - 2-0
Dicker - down the middle - 2-1
Lallana - low to the left, saved by Gillespie - 2-1
Joyce - low to the right, saved by Bogdan - 2-1
Coutinho - down the middle, superb save by Gillespie - 2-1
McQueen - thundering top corner drive - 2-2
Ings - down the middle - 3-2
Hery - low to the left, saved by Bogdan - 3-2
Liverpool - Ings (23)
United - Asamoah (35)
Liverpool - Origi (90)
Liverpool - Bogdan, Clyne (Ibe 86), Lovren, Milner, Firmino (Origi 35), Moreno, Lallana, Can, Allen (Coutinho 64), Ings, Skrtel. Subs - Fulton, Gomez, Brannagan, Rossiter.
Carlisle United - Gillespie, Miller, Raynes, Grainger, McQueen, Kennedy (Gillesphey 73), Dicker, Joyce, Sweeney (Ibehre 65), Hery, Asamoah (Gilliead 64). Subs - Hanford, Atkinson, Balanta, Archibald-Henville.
Referee - Mr Andrew Madley
Attendance - 42,518 (5,744 away fans)