Young, who has only just recently returned to action following a lengthy injury lay-off, scored United's first goal on 59 minutes before Hernandez added the second five minutes from time to give the English side a commanding advantage.
United had found themselves in European football's second-tier tournament following their shock failure to qualify for the knockout stages of the UEFA Champions League last December. Even so, United manager Sir Alex Ferguson stayed true to his pre-match pledge to take the competition seriously, naming a strong starting line-up to face the four-time European champions.
"I'm delighted with the scoreline," said Ferguson. "It was a very ordinary performance by us. We didn't reach any great heights in the game but we did improve in the second half and we deserved to win it."
Ferguson said Hernandez' late strike had given United a golden chance to advance to the last 16. "It gives us a good opportunity," Ferguson said. "We're not taking anything for granted but at home, at Old Trafford, we've now got a good opportunity to get through."
A low-key first half saw United start confidently, dominating possession and territory in the opening 20 minutes without seriously testing Kenneth Vermeer in the Ajax goal. Wayne Rooney was at the heart of United's best work, and had the English champions' first shot on goal after 19 minutes only for Vermeer to gather easily.
Moments later Rooney's weighted through ball helped Hernandez spring the Ajax offside trap but Vermeer was alert to the danger and was able to smother at the Mexican's feet. Hernandez had taken up a dangerous position in the Ajax box on 29 minutes as Nani ghosted down the right wing. To the visible exasperation of Ferguson on the touchline however, Nani went for goal, shooting high and wide.
On 32 minutes United were almost made to pay for their wastefulness, with Siem De Jong uncorking a ferocious right-footed shot from just outside the area which drew a superb diving save from David De Gea.
That effort lifted Ajax, and they had United on the back foot towards the end of the first half, with young Dane Christian Eriksen the next to test de Gea, with a swerving long-range effort. On the stroke of half-time, Ajax had penalty appeals waved away after Rio Ferdinand appeared to collide with Miralem Sulejmani on the edge of the area.
United regrouped after the break and were soon threatening the Ajax goal. Another perfectly weighted pass from Rooney split the Dutch side's defence and found Hernandez, but the striker was unable to get a shot off. Yet on 59 minutes United got the goal their bright start to the half had been threatening to deliver.
Nani's cross from the right flew across the penalty area and found Young on the opposite flank. The winger cut in and picked his spot before rifling his low finish beneath Vermeer and into the net.
With full-time looming Antonio Valencia pounced on a stray pass in midfield and released Hernandez. The Mexican fed Rooney and then gathered the English player's return pass to make it 2-0 and leave United with one foot in the last 16.