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Both sides traded blows without finding a knockout until 10 minutes before the break, as Odubajo's ferocious volley from outside the area put the Londoners ahead.
Orient then capitalised on the punch-drunk state of the Yorkshire outfit, with Odubajo turning provider to set up Cox for a simple tap-in to double the advantage minutes later.
Ben Pringle volleyed narrowly over the bar in the closing stages of the half to give Orient a warning of just how tenuous a two-goal lead is - and it proved a sign of things to come.
Rotherham emerged from the break reinvigorated and halved the deficit 10 minutes after the restart through Revell, who capitalised on Jones's failed punch to prod the ball into an empty net in scrappy fashion.
United then fed their London counterparts a dose of their own medicine by scoring again in quick succession, as Revell completed the comeback in fine fashion by firing an audacious volley over the head of Jones from well outside the area.
Chances were at a premium throughout the additional 30-minute period, meaning that the sides were forced to duke it out via penalties to determine who won promotion.
James Tavernier scored United's last to pile the pressure on Dagnall, and the striker then failed to beat Adam Collin from 12 yards as Steve Evans's side won promotion back into the Championship for the first time since 2005.