Making just his second appearance since December, Young netted his fourth goal of the season just before the hour mark, after good work from Nani.
United all but put the tie to bed five minutes from time as Hernandez tucked home, after substitute Antonio Valencia fed Wayne Rooney.
The win gives Sir Alex Ferguson's side a healthy lead going into the second leg in a week's time as the Scot attempts to win a trophy that has so far eluded him during his 25-year managerial career at Old Trafford.
Meanwhile, Ajax, off the pace in the Eredivisie, rarely threatened and have a mountain to climb if they're keep alive their only realistic hope of silverware this season.
Keen to bounce back from the humiliation of being dumped out of the Champions League at the group stage for just the third time in 17 years, Ferguson recalled Phil Jones, Ashley Young and Tom Cleverley, making his European debut, after lengthly absences.
Ajax, themselves knocked-out of the Champions League prematurely, began with Danish starlet Christian Eriksen, who troubled England in a friendly 12 months ago, while captain Jan Vertonghen, often linked with moves to Arsenal and Tottenham Hotspur, was charged with marshalling Hernandez and Rooney.
Following a cagey opening half an hour, the game sparked into life when Siem de Jong's long range strike brought the best out of David de Gea, before the Dutchman's header drifted over the bar.
United's threat in the first 45 minutes wavered, with Nani wasting several opportunities to deliver, while Rooney was unable to link effectively with strike-partner Hernandez.
However, early in the second half the pair combined to almost open the scoring as Kenneth Vermeer smothered Hernandez's close range effort.
But the visitors didn't have to wait long to grab a crucial way goal as Nani broke through the Ajax rearguard, and picked out Young, who after drawing Vermeer, drove United ahead.
The threat from Frank de Boer's side had diminished since the opening exchanges, but Eriksen's tricky run almost yielded an equaliser, but De Gea stood firm.
And with five minutes remaining, Hernandez tapped home, following Rooney's pass, to put the icing on the cake for United, as their first Europa League campaign for 15 years got off to the perfect start.