Two second-half goals from the two Red Devils attackers leave Sir Alex Ferguson's men in a commanding position going into next week's second-leg at Old Trafford
The match was one of two halves, with the home side dominating proceedings in the first 45 minutes while the Red Devils took the initiative in the second half.
Ajax was the brighter of the two teams in the opening 20 minutes, with the home side enjoying the larger share of possession. The reigning Dutch champions failed to create any clear cut chances however, with a weak shot from full-back Dico Koppers all they had to show for their controlled play.
United’s impressive attacking unit failed live up to their reputation with Hernandez caught in the offside trap on more than one occasion and Nani unable to conjure any form of danger from the right wing.
Ajax’s best attempt came in the form of a cracking effort by midfielder Siem de Jong. The Dutchman picked up the ball outside the box and released a curved right-footed effort, which David de Gea did well to palm away.
The resultant corner burdened United with more pressure, with De Gea nervously knocking out balls that ventured near his goal line. Christian Eriksen fired an attempt from range straight at De Gea a few minutes later.
The Red Devils started the second half with visibly more dynamism, surging forward in numbers and Nani looking slightly more threatening.
Rooney sliced a crisp pass through to Hernandez in the 50th minute, but the Mexican was not to be beaten by Vermeer, who charged out of his goal to deny the striker.
United did find the breakthrough in the 59th minute, after the Ajax defence failed to deal with a dangerous delivery into the box. The ball eventually fell to Young, who created space for himself inside the box and fired home through the legs of Vermeer.
End-to-end attacking play followed, with Ajax looking to level the score from range while United now looked the crisper side of the two.
Shots from Alderweireld and Eriksen did not trouble De Gea, but a great surge forward from the latter on an Ajax counter ended with a shot the Spanish stopper will have been happy to see fly straight at him.
It was Manchester United who found another breakthrough, however, as substitute Antonio Valencia found space for Wayne Rooney to surge into. The Englishman linked up neatly with Hernandez, who somewhat fortunately slotted the ball under Vermeer. The Dutch goalkeeper got a solid touch on the ball with his body, but the deflection could not parry the shot off target.
The result leaves Manchester United in the driving seat to progress, while Ajax will have to produce a remarkable comeback to reach the last 16.
The Amsterdam outfit will return to domestic duty before the second leg of the tie, with the reigning Dutch champions welcoming NEC to the Amsterdam Arena on Sunday. Manchester United do not travel to Norwich until February 26th, three days after the return fixture at Old Trafford.