Cheye Alexander and Matt McClure had given the hosts a two-goal lead with strikes in the 9th and 21st minute, but with six minutes of the first half remaining midfielder Craig Clay pulled one back with a header.
With time running out Orient managed to complete their comeback as substitute Boco calmly slotted home the equaliser on the 82nd minute.
On the back of Saturday’s 2-1 home defeat to Hartlepool United, Head Coach Steve Davis made three changes to the starting XI. Josh Coulson and James Dayton returned to the side following respective injuries, while loan signing James Brophy was also handed a starting berth following his arrival from Swindon Town on Thursday.
The O’s were without striker David Mooney however who missed out with a shoulder problem, while Josh Koroma missed out with a back injury despite a late fitness test. Matt Harrold also travelled with the squad to the Recreation Ground though missed out due to still recovering from a calf problem.
Sporting our new white third kit for the first time following Friday’s reveal, the O’s looked to get off to a flying start as Jobi McAnuff played in the returning James Dayton who dragged a shot wide of the far post before the flag was raised for offside.
McAnuff was operating in a different role to his normal one on the wing, playing just off forward Macauley Bonne and the pair combined well moments later before McAnuff was blocked off as he looked to get an early shot away.
Neither side had really troubled either goalkeeper during the opening minutes but Aldershot made the most of the first opportunity on the 9th minute as defender Cheye Alexander rifled home the opener which found the far corner despite Charlie Grainger getting a hand to the shot.
The goal appeared to knock the wind out of Orient, as Jim Kellerman first saw an effort held by Grainger before Matt McClure headed wide from a corner as the hosts pushed for a second.
McClure was then able to double the hosts advantage just after the 20th minute mark as he shrugged off Jamie Sendles-White on the corner of the O’s penalty area before smashing the ball beyond the reach of Grainger.
With the score at 2-0 it was Aldershot who looked to be in complete control, and James Rowe curled a 30th minute free-kick into the side-netting after Alex Lawless was penalised for a foul on Manny Oyeleke.
With 10 minutes remaining of the half it could have been three for the hosts as Rowe was left unmarked at the far post to meet a Kellermann cross, but Grainger reacted well to brilliantly parry the header around the post and following a scramble from the corner Aldershot could only poke the ball wide.
Needing a way back into the game, Orient then created their first clearcut chance of the afternoon on the 38th minute as McAnuff clipped a wonderful cross towards the far post which was met by Craig Clay who saw his header parried away by the Shots goalkeeper Jake Cole.
Clay was not to be denied a minute later however, as McAnuff was once again the provider by clipping a free-kick towards the far post for the midfielder to head home his second goal for the Club and set up a cagey final few minutes of the half.
Buoyed by the goal, Orient were left scratching their head as to how it 2-2 in first half stoppage time when a McAnuff free-kick came back off the post before Bonne was somehow denied by a spectacular save from Cole.
Having been encouraged by the performance towards the end of the half, Orient returned unchanged following the interval and started brightly as Brophy fired over before delivering a teasing cross which was just too far in front of Bonne.
It was a much improved display from the O’s following the first half showing, but despite moving the ball well the visitors were unable to trouble Cole in the Aldershot goal.
As the final 20 minutes approached, the Shots went in search of a third as Adam McDonell carried the ball forward before seeing a stinging shot parried away well by Grainger.
In response to the chance, Orient made their first substitution of the afternoon as Romuald Boco came on in place of Dayton in a move which saw the Benin international take up a role behind Bonne and McAnuff move out to the right wing.
Having been denied by Grainger only moments before, McDonnell took aim once again from outside the area on the 74th minute but his low shot whistled wide of the post.
Three minutes later it really could have been game, set and match for the hosts as Alexander’s cross found Kellermann unmarked in the box, but the O’s were left breathing a huge sigh of relief as his header dropped over the bar.
The miss was to prove costly for the hosts, as with eight minutes remaining Orient found an equaliser as Boco proved to be a super sub by pouncing on a defensive error to round the ‘keeper and slot into an empty net.
There was a slight dampener after the goal however, as Josh Coulson was forced off through injury and subsequently replaced by Dan Happe for the final moments.
Five minutes stoppage time was shown by the fourth official, and with two of the five remaining the O’s almost snatched the victory as Bonne first saw a shot cleared in the area before Clay’s header was clawed off the line from the resulting corner as both sides settled for a point at the Recreation Ground.
ALDERSHOT: Cole, Alexander, McDonnell, Reynolds (C), Arthur, Fowler, Oyeleke (Robert 79), Gallagher, Rowe, Kellermann, McClure (Rendell 70)
SUBS: Smith, Okojie, Lyons-Foster
GOALS: Alexander (9), McClure (21)
BOOKED: Alexander (53)
ORIENT: Grainger, Caprice, Coulson (Happe 84), Sendles-White, Widdowson, Lawless (C), Clay, Dayton (Boco 72), Brophy, McAnuff, Bonne
SUBS: Sargeant, Ochieng, Dalby
GOALS: Clay (39), Boco (82)
BOOKED: McAnuff (81), Bonne (88)
REFEREE: David Rock
ATTENDANCE: 3,060 (566)