Danny Cashman gave the Seagulls a deserved first-half lead but Orient were the more threatening side after the break and equalised through Louis Dennis.
So it finished 1-1 after 90 minutes and Orient picked up the bonus point by winning the subsequent shoot-out 4-2, although Albion finished the group stages unbeaten following earlier wins over AFC Wimbledon and Southend.
The visitors made the early running with Peter Gwargis testing O’s keeper Sam Sargeant with a shot from distance in the sixth minute.
Ben Wilson thought he had put the visitors in front six minutes later, when he turned home the loose ball after Cashman’s drive from the edge of the box came back off the right-hand post, but the assistant’s flag was up for offside.
Orient had their moments with James Alabi lively in midfield but the Seagulls’ ball retention was better and they continued to threaten. Sargeant had to shovel the ball around the post for a corner when Gwargis let fly, having seen his free-kick blocked by the wall.
But Albion finally broke the deadlock on 33 minutes and it was a superbly-worked goal. Teddy Jenks collected possession and ran at the home defence before finding Cashman who had cleverly found space inside the box and fired emphatically past Sargeant from 12 yards.
David Button was finally called into action on 40 minutes when he dived to his left to keep out a free kick from former Albion midfielder Jordan Maguire-Drew, but the visitors had controlled the first period.
Orient began the second half brightly. Alabi shot wide from a decent position and Haydon Roberts picked up the game’s first yellow card for a foul as the hosts looked for a way back into the contest. Dennis shot wide from close range after good work down the right by Myles Judd as Albion struggled to rediscover their first-half fluency.
The equaliser came on 64 minutes. Maguire-Drew crossed from the right and Dennis stole a yard on his marker to beat Button with a header from point-blank range.
Albion nearly produced the perfect response with skipper Alex Cochrane hitting a free kick from just outside the box a yard wide of the left-hand post but Orient nearly scored again with nine minutes remaining after a cross-field move ended with James Dayton’s left-foot shot hitting the outside of the post from Maguire-Drew’s cross.
Back came Albion and Cashman thought he’d scored his second on 84 minutes with an effort that was heading for the bottom corner until Marvin Ekpiteta’s deflection took it wide of goal. Orient then struck the woodwork again with Maguire-Drew’s curling effort flicking the top of the crossbar.
The hosts piled forward in stoppage time but Albion dug deep. Antef Tsoungui made two blocks on the line to deny Maguire-Drew and Dennis before Alabi’s shot was touched onto the post by Button.
So to penalties. Button saved from Dennis but both Cochrane and Jenks saw their efforts kept out by Sargeant. Archie Davies and Button did score for Albion, but Alabi’s spot-kick, which went in off both posts, secured the extra point for the O’s.
Albion line-up: Button; Davies, Tsoungu, Roberts (Leonard 89), Cochrane ©, Gwargis, Jenks, Baluta, Richards (Yapi 86); Cashman, Wilson (Vukoje 71).
Subs not used: McGill, Radulovic, Cocoracchio, Leahy.