Alan Curbishley's Addicks side won promotion to the Premier League with one of the greatest ever play-off finals in 1998, beating Sunderland on penalties after drawing 4-4.
This final will not be ed in the same way.
The game's big moment came after half an hour of largely forgettable football when former Charlton defender Rarmani Edmonds-Green, who moved to the O's in the winter transfer window, fouled Tyreece Campbell on the edge of the area.
With Alex Gilbert standing over the ball, Gillesphey stepped up to send a curling free-kick away from the dive of Josh Keeley, who could only get his fingertips to the ball before it nestled in the back of the net.
The O's goalkeeper had left a large space to his left for the Addicks defender to aim at, with the wall looking like an extra player was needed to provide enough cover.
Orient were much improved after the break as they attacked the end housing their fans, with Jack Currie deflecting a shot narrowly wide before Jordan Brown fired just over the bar.
Kelman came closest as his deflected effort from outside the box flipped up off the top of the bar.
A lengthy stoppage needed for referee Andrew Kitchen to resolve a technical issue with his video assistant referee (VAR) headset led to 11 minutes of added time.
Substitute Dan Happe's looping header looked to be Orient's final chance, as the ball looped up and into the grateful arms of Charlton keeper Will Mannion.