Goals by Wayne Rooney, Ruud van Nistelrooy and Cristiano Ronaldo in the first leg of their Champions League third qualifying round first leg clash at Old Trafford should ensure their passage into the lucrative group stage of the competition.
Debreceni will have to create more than a 67th minute free-kick by Tamas Sandor, which was easily taken by United's new £2million keeper Edwin Van der Sar, if they are to worry the Reds Devils in the second leg.
It took United only seven minutes to break down their pedestrian opponents.
Ronaldo's ball to van Nistelrooy in the Debreceni box came back to Rooney off two defenders and he rifled in a sweet right-foot shot from 12 yards.
United continued to probe the Hungarians but their only other clear-cut chance of the first half came when Ronaldo's crisp 21st minute effort was saved by Debreceni goalkeeper Norbert Csernyanszki with his legs.
United's European talisman van Nistelrooy made it 2-0 four minutes after the interval.
As Rooney raced towards the Debreceni box, he played a perfectly waited pass to van Nistelrooy who was overlapping to his right and the Dutchman scored with a low drive from 12 yards.
Csernyanszki did well to keep out a curling free kick from Ronaldo but he was powerless to stop United's third goal in the 63rd minute.
Van Nistelrooy fed Rooney on the right side of the Debreceni penalty area and he whipped the ball back into the centre for Ronaldo to score with a low right-foot shot from close range.
Ji-Sung Park, United's £4million close season signing from PSV Eindhoven, replaced skipper Roy Keane after 68 minutes and he came close to scoring in the dying seconds when his deflected shot from the edge of the Debreceni penalty area was well saved by Csernyanszki.