After a lackluster first half from both teams, Young profited when he latched onto a cross from Nani, cut inside right back Vurnon Anita and fired a low shot under goalkeeper Kenneth Vermeer in the 59th minute.
Hernandez set up a comfortable second leg for United when he played a one-two with Wayne Rooney and fired home five minutes from fulltime.
Ajax and United have been crowned European champions seven times between them, but are playing in the continent's second-tier competition after being eliminated from the Champions League at the group stage.
Manchester was without captain Patrice Evra, who was rested by Alex Ferguson to give him time to recover from an ''emotional'' week following his spat with Luis Suarez. Evra was snubbed by Suarez in the pre-match handshake before United's match with Liverpool on Saturday, their first meeting since the former Ajax striker was banned for eight matches for racially abusing Evra during a game.
Plagued by injuries this season, Ajax was playing with a patched-up defense, midfield and attack but still had the best of the first-half chances.
United looked nonchalant before the break and Nani squandered the team's only clear-cut chance when he blasted a shot high and wide of the goal from the right of the penalty area with an unmarked Rooney calling for a cross in the middle.
Midfielder Siem de Jong came closest for Ajax before the break with a powerful shot that forced a good save from David De Gea diving to his left in the 32nd. Two minutes later, De Jong was again threatening when he rounded off a spell of Ajax pressure by heading a cross over the bar.
Ajax had an appeal for a penalty turned down on the stroke of halftime when Rio Ferdinand appeared to bring down Miralem Sulejmani on the edge of the box.
United began the second half far more aggressively and Nani almost immediately hit a stinging shot that Vermeer tipped over the bar.
As United turned up the pressure on the makeshift Ajax defense, Fernandez turned away from Anita in the 50th but Vermeer dived at his feet to deny the Mexico striker.
United's second-half dominance paid off in the 59th with Young's goal, but United then sat back and allowed Ajax into the game.
Aras Ozbiliz nearly hit back immediately for Ajax, but sent his dipping left-foot shot just over the bar after dispossessing Fabio, and midfielder Christian Eriksen had a good scoring chance in the 73rd but shot straight at De Gea after a strong solo run.
But as Ajax pushed for the equalizer, Hernandez and Rooney combined on the break to make it 2-0.