Benicio Baker-Boaitey drew Albion level midway through the first half after Diego Moreina had put Chelsea in front.
Dujuan Richards restored Chelsea’s lead after Tom McGill had kept out his penalty and added his second on the hour to make it 3-1.
It looked like Albion’s race was run but substitute Josh Duffus got us back into it with a header and defender Leigh Kavanagh lashed in the equaliser with five minutes to go.
Chelsea restored their lead in the first period of extra time through Jimmy Jay-Morgan but back came Albion again to level for a third time through Duffus.
Albion looked more likely to win it in extra time but with penalties looming Zain Silcott-Duberry won it with an intuitive finish from outside the box.
Albion had a good chance inside the first minute but Louis Flower, against his old club, headed Luca Barrington’s right-wing cross just wide.
The visitors began brightly but slowly Chelsea started to take control. Lee Castledine should have at least hit the target with a glancing header from close range in the 18th minute but directed it wide and it needed Ruairi McConville to make a crucial block on Tyrique George’s powerful hit.
A Chelsea goal looked like it was coming though and it arrived on 22 minutes. George attacked the space after Albion conceded possession in midfield before finding Moreina on the left. He cut inside onto his right foot and fired powerfully past Tom McGill.
McGill was forced to back-pedal to save after George had fired towards goal from 40 yards but seconds later the Canadian keeper had instigated the equaliser. Baker-Boaitey latched onto his long clearance down the middle and rounded Chelsea keeper Max Merrick and stroked the ball into the empty net.
Albion deserved to be level but Chelsea’s attacking players were lively and when Ruairi McConville tripped Richards in the box they had a penalty. McGill plunged to his left to push out Richards’ effort but the Chelsea player followed up to score and just before the break Moreira nearly got a second only to guide a close-range shot inches wide.
Albion were the more threatening on the resumption and McConville guided a free header from Kamari Doyle’s cross over when he ought to have hit the target. Caylan Vickers’ shot only just cleared the bar but on the hour Chelsea stretched their lead when Richards curled a left-foot shot inside the far post from the edge of the box.
But once again Albion hit back. Luca Barrington picked out substitute Duffus with a lovely cross from the left which he headed powerfully past Merrick with 18 minutes to go.
The momentum was now with the visitors and they deservedly drew level in the 85th minute when Barrington’s corner dropped for defender Kavanagh to lash the ball into the roof of the net.
Albion carried the greater threat in the additional 30 minutes with Merricks making a superb save with his feet to deny Duffus.
Not surprisingly the game got very stretched and the teams traded further goals in added time at the end of the first period of extra time. Substitute Morgan converted a cross to restore Chelsea’ lead but moments later it was 4-4 when Duffus found the bottom corner after good work by Vickers.
Duffus was denied his hat-trick by another fine stop from Merricks who somehow kept out his close-range shot and just how important a save that was became evident with three minutes to go when substitute Silcott-Duberry spotted McGill off his line and lifted a right-foot shot from 25 yards over the stranded keeper and into the empty net.
Albion: McGill, Jackson (Nilsson 61), McConville, Kavanagh, Barrington, Chouchane, Doyle (Albarus 81), Slater, Vickers, Baker-Boaitey (Duffus 61), Flower (Peart 72).
Subs not used: Hall.