The victory reignited Orient's promotion push and pushed them up to 10th in the table as Notts County's recent good run came to an abrupt end with their second defeat in the space of five days.
Youngs, signed from Northhampton Town 24 hours before the game, made an immediate impression with a right-wing cross in the sixth minute that Andy Scott headed just wide. But it was Notts County who weathered the early storm and had the best chance of the first half when Gavin Gordon sent a header against the Orient bar and home goalkeeper Lee Harrison blocked Paul Bolland's follw-up attempt.
Gordon also headed over on the stroke of half time but it was not all one way traffic and as Scott had gone close to breaking the dead lock on 38 minutes. His first effort was blocked by Notts County keeper Saul Deeney and his follow-up effort was desperately blocked by a defender.
Orient finally made their pressure count on 56 minutes when Michael Simpson's through ball was chested down by Scott and Youngs needed no second invitation to fire home from 20 yards.
Goal hero Young left the field to a standing ovation, eight minutes from time and it was his replacement Barnard who made the game safe with a second goal.
O's strung together a series of passes that ended with Simpson playing against his former club, sending his ball across the area for Barnard to fire home at the far pot, it was the defenders first goal of the season and only the second of his career.