Chesterfield were the better side in the opening exchanges, their width provided by a 4-4-2 formation allowing debutant Mark Duffy to make instant inroads.
The Spireites took the lead on 18 minutes, when Caolan Lavery was pulled down while chasing Jimmy Ryan's pass. O'Shea quickly stepped up, and sent Orient keeper Alex Cisak the wrong way.
Orient looked sharper after the setback, and drew level when Chris Dagnall squared having broken the offside trap, allowing Mooney to stroke home from six yards out.
The hosts regained the advantage in bizarre fashion 10 minutes after the resumption, when Armand Gnanduillets cross from the byline was volleyed with aplomb into his own net by the hapless Omozusi.
Chesterfield looked more likely to move up the gears, but Orient pegged them back out of nothing with 20 minutes to go, Mooney clicking on to a long ball and lashing in from 16 yards.
A remarkable eight minutes of stoppage time - lengthened after Ian Evatt suffered a head injury - didn't look like it would produce a result, until Tommy Lee dropped a routine cross at the foot of Dean Cox, who won three unlikely points for Orient.