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Ebbsfleet are two wins from the Football League after knocking Aldershot out of the play-offs in sensational style.
They were 1-0 down with a minute to go in extra time but Dave Winfield's header sent the tie to penalties.
Fleet then trailed 3-1 in the shoot-out but Nathan Ashmore saved Aldershot's last kick of the five before Dean Rance stepped up to win it.
Ebbsfleet's only change came at left-back, where Jack Connors was preferred to Chris Bush, while Aldershot went attacking as Scott Rendell started alongside Kabamba and Matt McClure.
The home side dominated the first half but only forced one meaningful save from Nathan Ashmore as Fleet's defenders stuck to their task well.
Luke Coulson hooked a volley wide from Lawrie Wilson's cross and Corey Whitely had a low shot saved by goalkeeper Lewis Ward as the visitors enjoyed some good possession in the Shots half.
But Aldershot's front three of Rendell, Kabamba and McClure certainly gave the visitors plenty to think about and when Ashmore got a hand to Kabamba's low strike from the left-hand side of the box, Connors had to be alert to clear the loose ball.
Jake Gallagher went close twice in as many minutes although his second shot followed a strong challenge on Coulson which angered the away supporters and left Coulson needing treatment.
Aldershot were building up a head of steam and Fleet were guilty of giving the ball back to them too cheaply.
Gallagher's cross was headed over by McClure and Rendell had a shot blocked after Kabamba was allowed far too much room to bring down a long ball out of defence.
Fleet's backline was really being tested and they blocked another Gallagher strike before a Rendell header dropped onto the roof of the net after he'd got up above Wilson.
When Ebbsfleet did get forward, a cross from Connors drifted harmlessly behind and back came the home side.
McClure walked into a good position and forced another good block as Fleet dug in.
The last few minutes of the first half were a little less anxious as the men in yellow held onto possession better without troubling Aldershot.
Their best move saw the ball worked right to Wilson but his cross, although it reached Powell in the middle, was directed tamely into Ward's gloves.
Ebbsfleet maintained a good shape at the start of the second half and Adam McDonnell's hopeful effort from distance sailed wide.
The game exploded into life on 53 minutes following a good spell for the visitors.
Kedwell was played clear in the box and when he went down under Callum Reynolds' challenge, referee Alan Young pointed to the spot.
A melee ensued and Kedwell had to wait an age to take his spot-kick, which was saved by the legs of Ward.
That got the home crowd going and when substitute Jim Kellermann surged through midfield, McClure forced a save from Ashmore. Drury was then fouled in the process of making a crucial clearance.
But, led by centre-halves Dave Winfield and Kenny Clark, the visitors stood tall at the back. Clark made an immense block to deny Kabamba just as he was about to get a shot away.
There was a lengthy delay while Kellermann received treatment for an injury sustained in the process of tugging Dean Rance's shirt.
Kellermann was eventually stretchered off, wearing an oxygen mask, as the home side were forced to make their final change with 14 minutes of the 90 remaining.
Aldershot seemed to be running out of ideas and McDonnell lashed a long shot a long way wide of Ashmore's goal.
The home side were hanging on during nine minutes of stoppage-time but Fleet couldn't make a series of corners pay and the tie went into extra time.
Both sides looked leggy now and McDonnell bent a shot wide from distance before Myles Weston failed to pick out Kedwell, unmarked in the middle, when Ebbsfleet broke.
Whitely pulled up at the end of the first extra period and Marvin McCoy was sent on for the final 15 minutes.
The home side finally broke the deadlock in the 106th minute when Kabamba sent a glancing header from Cheye Alexander's cross into the top corner.
But there was incredible drama with just two minutes left when Rance's hanging cross was headed home by Winfield at the far post.
McCoy and Powell both had penalties saved by Ward in the shootout to leave Aldershot with two chances to win it.
But after Kinsella hit the post, Ashmore saved from Fabien Robert and Rance held his nerve to send Fleet through to a semi-final at Tranmere.
Aldershot: Ward, Alexander, Evans, Oyeleke, Rendell, McClure (Robert 66mins), Kabamba, Gallagher (Kellermann 58mins, Rowe 76mins), McDonnell, Kinsella, Reynolds. Subs not used: Cole, McQuoid.
Ebbsfleet: Ashmore, Wilson, Winfield, Clark, Connors, Rance, Drury (Wabo 108mins), Whitely (McCoy 105mins), Powell, Coulson (Weston 90mins), Kedwell. Subs not used: Miles, Bush.
Attendance: 3,319 (483 away).