The last time Young found the net was a last-gasp face-saver against Basel at Old Trafford, in a match which Sir Alex Ferguson still looks back on as the draw that cost his team their place in the Champions League.
And, after a poor first-half, the visitors roused themselves after the break and Young's 58th-minute winner came at the end of their most threatening spell, the England man tucking home after Nani's cross had been deflected into his path.
Javier Hernandez added a second six minutes from time to secure a result that will allow Ferguson to take a pragmatic approach to next week's second leg, which, unlike tonight, will be followed four days later by a crucial Premier League game, against high flying Norwich at Carrow Road.
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 Ashley Young only just returned from a pre-Christmas injury, it was perhaps no surprise United were so far off the pace.
Too many first touches and passes went astray. Crossing was a particularly bad area.
Nani sent one corner straight out for a goal kick, failed to pick out a team-mate with one obvious cross and then smashed a shot into the side-netting from an impossible angle as Wayne Rooney and Javier Hernandez screamed for a pass.
On the other flank, Young fared only marginally better and though Cleverley flickered, he could not sustain his impact for any length of time.
As usual then, Rooney was the visitors' main threat, although his 25-yard effort lacked the venom to beat Kenneth Vermeer with the best chance of that tepid opening period.
Ajax played the kind of free-flowing passing football for which Holland is renowned.
Christian Eriksen may be a Dane but it was easy to see why he chose Holland to learn his trade rather than expose himself to the physicality of the Premier League.
Eriksen prodded and probed and tested David de Gea with a couple of pot shots.
Siem de Jong came closest to breaking the deadlock though, also from long-range.
The wide-man's shot was on target though and De Gea needed to stretch to keep it out.
When United last appeared in a European game outside the Champions League, goalkeeper Peter Schmeichel was amongst the scorers.
De Gea never contemplated emulating the great Dane. His stock is starting to rise though and Ajax refused to reduce themselves to pumping their opponents' box with crosses in an effort to expose the Spain star's weakeness under a high ball.
That there was no injury-time reflected a general lack of first-half excitement.
There as a talking point in the final minute though when Miralem Sulejmani went down under Rio Ferdinand's challenge.
Ajax were convinced it was a penalty. Italian referee Gianluca Rocchi decided otherwise, leaving Ferdinand to hobble down the tunnel for his break.
Stand-in skipper for the night in place of an emotionally drained Patrice Evra, Ferdinand was able to return for a second-half United began with far more zip than they had shown previously.
Jan Vertonghen was at full stretch to prevent Young's cross reaching Jones at the far post and Vermeer and Vurnon Anita combined to snuff out an opening that seemed to be presenting itself to Hernandez.
United were definitely turning the screw though and it was no surprise they broke the deadlock just before the hour.
So frustrating so often, Nani for once managed to find a team-mate with a cross that flicked off an Ajax defender.
Young steadied himself after beating Anita, eventually drilling a low shot through a crowd of bodies.
It was the former Aston Villa man's fourth goal since his £18million summer move to United and was followed immediately by Cleverley's departure for Paul Scholes, in the absence of Ryan Giggs the only remaining member of that 1995 UEFA Cup team.
Antonio Valencia's introduction for Young provided the South American with enough time to begin a move that ended with Hernandez exchanging passes with Rooney before slotting home his third goal in as many games and ninth of the season.
Valencia was instantly replaced after taking a knock in the build-up, although it only appeared to be a precaution.
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