The former Nottingham Forest striker marked his first start for the O's with an impressive display before substitute Kevin Lisbie rounded off the win with his first touch.
Oldham went in front after 16 minutes as Carl Winchester's neat pass found Jonathan Forte, who strode clear of the Orient defence and slotted in from 14 yards.
But the visitors levelled only four minutes later when Henderson ran on to Dean Cox's throughball and steered home a low finish from just inside the box.
Oldham wasted two chances before half-time, with Mike Jones firing wide at the end of a flowing move and Liam Kelly heading off target.
They were punished by Orient's second goal, in the 58th minute, as Henderson teed up David Mooney to drill in an angled shot from eight yards.
James Wilson headed over for Oldham, but Lisbie killed off the game within seconds of replacing Henderson in the 80th minute.
Lisbie met Cox's corner and completed Orient's fightback by nodding home from close range.