The hosts had an early claim for a penalty ignored when Bradley Wright-Phillips went to ground under a challenge from Orient goalkeeper Paul Rachubka.
But Chalrton did not have long to wait to get their noses in front, taking the lead in the seventh minute when Wagstaff tapped home Rhoys Wiggins' low cross after a quickly-taken free-kick.
Only a last-gasp clearance off the goalline by Wiggins prevented Ben Chorley's 25th-minute shot from putting the visitors back on terms, but Orient protested furiously that the ball had been handled.
Rachubka pulled off a stunning double save within six minutes of the second half by making a one-handed stop from Wright-Phillips and then reacting quickly to prevent Lee Cook firing in the loose ball.
Former Addick Kevin Lisbie twice went close to equalising for the visitors in the second period, but Charlton wrapped the points up in the 81st minute as N'Guessan headed past Rachubka after meeting Cook's cross.