United were made to feel extremely welcome from the off at the SkyEX London Community Stadium with the only ingredient missing the supporters for this round one Emirates FA Cup tie.
Manager Chris Beech made five changes from Tuesday night's Newport home game with Marcus Dewhurst, Jack Armer, Dean Furman, Gavin Reilly and Omari Patrick elevated to the starting eleven.
For Sheffield United loanee Dewhurst it was a first start for the club, and a first start for Omari Patrick since he dropped out of the fold through injury 10 games ago.
Some 74 places separate the sides in the football pyramid, but with a host of scalps already taken during the Saturday run of fixtures there was nothing at all being taken for granted by the League Two contingent.
And that proved to be the right approach as they were taken to the wire by a spirited home performance.
The Blues had an early corner as a flick from Reilly hit Downing and went behind, but Smith was off his line smartly to claim the delivery.
A long throw from Kayode brought away shirts forward but the initial touch went high and the keeper was able to make it his.
Striker Omari Patrick went into the book for a heavy challenge on Norville-Williams inside the first 10 minutes, but United were back on the front-foot from the restart with Reilly winning another corner.
Riley sent it in, Hayden nodded it on and Reilly was a whisker away as he hooked the ball over his shoulder and just over the bar from eight yards out.
Another Riley set piece caused all kinds of problems as it fell in front of Hayden and Mellish, but strong defending meant that no shot could be completed.
Carlisle bided their time and they broke at pace when Hunt cleared a long throw from Robinson towards the halfway line. Reilly clipped it for Kayode to chase, and Tanner overlapped before rolling it back towards the edge of the area. Midfielder Joe Riley went for a first time strike but he couldn't keep it down.
United worked a way through when they set another attack in play from deep. Riley put Patrick away, and he bounced the ball to Mellish who was suddenly through. He went for the far corner from a tight angle but Smith was equal to it.
An overlap from Amartey saw him make space for a cross at the other end, but Hunt had positioned himself well to make an important clearance.
The hosts came again on 22 minutes when Downing sprinted with the ball at his feet. His cross was dangerous but Dewhurst watched it all the way.
Jon Mellish showed that he had his shooting boots on midway through the half when he latched onto the ball 25-yards out. His effort had power and Smith had to tip it over the bar.
United came again from the corner and Kayode was up highest to meet the cross. He aimed for the far corner but it looped onto the roof of the net.
The Cumbrians stayed forward and another Kayode long throw was trapped by Hayden. He tried to smash it on the swivel but he got his angles wrong and he could only poke it wide.
There was a real scare for the visitors on 32 minutes when Norville-Williams sent a perfect cross into the mix. The prolific Francis Amartey suddenly had just Dewhurst to beat but the stopper spread himself and he was relieved to be able to gather the volley into his chest.
Drama came at the other end when Hunt and Reilly worked a gap for Riley to shoot. He unleashed a real thunderbolt from distance and he couldn't believe his bad luck as it rattled down off the underside of the woodwork with Smith beaten all ends up.
A fourth goalmouth scramble for the away side came to nothing, after Patrick had kept a shot low, with Hayden judged to be offside as he spun to finish it off.
The visitors were almost gifted a goal just before the break when a headed pass from Kayode caused confusion between McDevitt and Robinson. The latter hesitated on a clearance and he looked on in horror as his eventual attempt at a punt came back off the onrushing Omari Patrick. It swirled over the keeper's head and just past the upright.
United fashioned the first chance after the break when a tussle between Riley and McDevitt saw the ball break for Furman, who had crept forward from a midfield berth. He set himself before forcing a superb diving save from Smith as his 20-yard shot arrowed towards the top corner.
A long kick followed and Amartey shrugged Hayden out of the way before bearing down on Dewhurst. The keeper stayed big to make a vital save.
Back at the other end and a floated pass from Kayode found Mellish with his back to goal. His cushioned moment of control invited Patrick to shoot, but it lacked power and the stop was easy to make.
An excellent chance was created by the away side when Tanner overlapped before beating his man. He streaked into the area and cut the ball back, where Patrick was lurking. He opted to shoot first time, but he couldn't keep it down and it sailed high over the bar.
A surge from Patrick from deep inside his own half won the Blues a corner just before the hour, and the ball had to be cleared off the line as the Riley inswinger was allowed to bounce. Reilly stretched to head it, and he thought he'd done the trick as it threatened to loop beneath the bar. A timely header prevented the goal.
Furman and Patrick had further speculative efforts, with Smith comfortable for both, and loud appeals for a penalty were ignored on 67 minutes when Kayode tumbled to the floor as he tried to twist into space.
The home team were then turned inside out when Riley released Tanner on the right flank. The low cross took a deflection off Williams and that was enough to take it away from the line of incoming strikers.
Amartey was convinced he also had a penalty claim as he fell to the floor under pressure, but Carlisle ignored the remonstrations as they broke free. Riley had a 19-yard free kick blocked, and Patrick had one cleared off the line when he dug a corner out of his feet to send a drive at the bottom corner.
Hunt put a Guy corner wide as the clock ticked down, and a great chance went begging on 82 minutes when a Kayode header sat up nicely for Reilly. He took it on his chest, turned away and had just Smith to deal with as he approached the penalty spot. His cruncher appeared to be going in until it bounced back to safety off the base of the post.
Hayes almost snatched it in time added on when Williams backheeled Robinson into a crossing position. Amartey threw himself at it but Hayden was there to make the intercepting header before the striker could pounce.
The first period of extra time started with a Carlisle attack with Kayode taking a pass from Anderton on his chest. He stepped on from his marker and let one go, but Smith threw a hand up to divert it away.
But it was Hayes who grabbed the lead on 104 minutes when Omar Rowe took the game to the visiting defence. A ricochet went the way of Downing, who was up in support, and he fed it back to Rowe who calmly dropped a shoulder before poking his effort into the bottom corner.
Substitute Amos Nasha doubled the lead with a stunning goal on 108 minutes, but a late brace from Jon Mellish took the tie to penalties as he first rattled one home from distance, before spinning on the spot to clip a close-range equsaliser into the bottom corner with almost the last kick of the game.
A thrilling penalty shoot-out followed, with Dewhurst saving excellently to set up the win for the away side. Gav Reilly did the honours to back that up as he stroked the decisive penalty into the back of the net.
Gaifiti scores 1-0
Mellish scores 1-1
Williams saved 1-1
Anderton scores 1-2
Nasha scores 2-2
Alessandra misses 2-2
Robinson saved 2-2
Tanner scores 2-3
Rowe scores 3-3
Kayode saved 3-3
McDevitt misses 3-3
Reilly scores 3-4
Hayes & Yeading United - Rowe (104), Nasha (108)
Carlisle United - Mellish (118, 120)
Hayes & Yeading United - Williams (17), Rowe (40), McDevitt (72), Sheppard (84)
Carlisle United - Patrick (8), Furman (76)
Hayes & Yeading United - Smith, Downing (Johnson-Schuster 120), Norville-Williams, Williams, McDevitt (c), Robinson, Rowe, Sheppard (Gafaiti 115), Cunningham (Donnelly 69 (Nasha 95)), Amartey, Odelusi. Subs - Lavin, Bajja, Hanlon.
Carlisle United - Dewhurst, Tanner, Hayden (c), Hunt, Armer (Anderton 90), Riley (Alessandra 102), Furman (Guy 78), Mellish, Kayode, Reilly, Patrick (Obiero 83). Subs - Farman (gk), Charters, Malley.
Referee - Ollie Yates
Assistant - Louis Marks
Assistant - Geoffrey Russell
Fourth Official - Daniel Lamport
Attendance - BCD