The reverse fixture saw the O’s run out 1-0 winners on the first day of the season when Jaedon Phillips grabbed the winner back in August.
Hector Kyprianou’s second half goal gave Orient the lead before Leroy Hlabi’s equaliser minutes later meant the two sides shared a point.
Orient got the game underway in cold and windy conditions in Gillingham, but it was the hosts who had the first attempt on goal when a whipped cross from the right was inches away from connecting with the boot of the striker after he threw himself at the ball six yards in front of the net.
The O’s had to withhold some pressure from the hosts early on, as they enjoyed possession in the Orient half before a Gills midfielder dragged a shot wide just after 10 minutes of play.
The hosts continued to search for an opener and thought they found one when a header at the far post from a wide free-kick was chalked out for a foul-on O’s captain Teddy Perkins.
Some good work by Leroy Hlabi on the right wing allowed the midfielder to create space to cross for striker White as the far post, whose header set up a team-mate for a shot which is quickly charged down by the O’s defence.
Moments before the break, Arthur Janata was at full stretch to cover his net when a spectacular effort from 20-yards whistled inches over the crossbar.
The O’s took the lead just after 60 minutes after Charles Clayden’s corner was punched in to the air by The Gills ‘keeper before Hector Kyprianou was on hand to lash home a volley from close range.
However, the lead wasn’t to last long when a cross from the right was blocked by Shadrach Ogie it fell to Hlabi who volleyed the ball just inside the near post to level the scores.
Orient were not disheartened by the goal however as they attacked straight down the other end and almost added a second when Ernold Haxhiu set Sam Dalby up for a shot inside the box, but the strikers attempt rebounded off the post and in to the hands of the Gills ‘keeper.
The hosts attacked down the right wing again when a cross/shot looped goal-wards and forced a good reaction save from Janata to palm the ball over his crossbar, which saw the game draw to a level ending.
ORIENT: Arthur Janata, Andrew Camilo-Tayaca, Mason Hall, Teddy Perkins (Alfie Fleming 55), Shadrach Ogie, Jaedon Phillips (Eric Lopes 25), Ernold Haxhiu, Hector Kyprianou (Brendon Shabani 83), Charles Clayden, Amin Benyoucef, Sam Dalby.
SUBS: Sam Amedu, Luca-Carter Henry
GOALS: Kyprianou (60)