Although the hosts were dominant in the first half, the visitors roused themselves after the break and Young's 58th-minute strike came at the end of their most threatening spell, the England man tucking home after Nani's cross had been deflected into his path.
Hernandez added a second six minutes from time to secure a result that will allow manager Sir Alex Ferguson to take a pragmatic approach to next week's second leg.
As Tom Cleverley was handed his European debut after playing just twice since the beginning of September and not at all for over three months, Nani and Phil Jones back after four-match absences and Young only just returned from a pre-Christmas injury, it was perhaps no surprise United were so far off the pace.
Ajax made a composed start, enjoying plenty of possession. However, Dimitri Bulykin was unable to find star man Christian Eriksen with a lay-off on the edge of the box.
Siem de Jong drew an excellent save out of David De Gea with a 30-yard strike that was heading into the corner, while the United goalkeeper was also on hand to collect Toby Alderweireld's knock-back, then De Jong got on the end of Miralem Sulejmani's cross but could only steer his header over the bar.
The hosts thought they should have had a penalty when Sulejmani went down under Rio Ferdinand's challenge in the final minute of the half. However, referee Gianluca Rocchi waved away the protests as Ferdinand hobbled down the tunnel at the break.
The defender was able to continue after the interval as United started brightly, Nani forcing a decent save out of Vermeer. And, after failing to create anything from a couple of decent crossing opportunities, United opened the scoring when Nani's cross flicked off an Ajax defender to Young.
The England man steadied himself before drilling a shot through a crowd of bodies.
Antonio Valencia replaced Young, although by now United seemed content to try and catch their opponents on the break. And they did exactly that six minutes from time when Valencia released Hernandez, who then exchanged passes with Wayne Rooney before firing home.
Source: PA
Source: PA