This was a clash of two of the early season form teams in League Two but, despite its billing, the contest never really got going.
The visitors took charge of the first half and settled quickly into a neat pattern of passing with wide men Donny Barnard and Aiden Palmer prominent.
They grabbed the lead with 20 minutes gone when a right-wing corner taken by Daryl McMahon was only partially cleared as far as Craig Easton to the left of the penalty area. His cross was turned in by defender John Mackie at the near post.
Cheltenham goalkeeper Shane Higgs then dived to parry a powerful low shot from Gary Alexander as the O's maintained their grip on the early part of the game.
The home side struggled for any fluency and their only first half chance of note arrived shortly before the break, midfielder JJ Melligan forcing a flying save from Orient goalkeeper Glyn Garner with a 30-yard shot.
Cheltenham upped their game in the second half but could find no way past an Orient defence in which young centre-back Gabriel Zakuani was outstanding.
On the rare occasions the Robins managed to pierce the Orient back line their finishing was found wanting.
A fine solo run by Melligan ended with a low drive that was blocked by Garner, and then three headed chances were spurned in quick succession. Kayode Odejayi, Damian Spencer and, most glaringly of all, Brian Wilson were the culprits.
Orient appeared to have three points in the bag until a left-wing cross from Melligan was cleared only as far as Finnigan on the edge of the box two minutes into added time.
Finnigan drilled his shot back at goal and it took a deflection on its way past Garner.