The former England midfield man, who will be 32 next month, scored with the sweetest of right-foot shots in the 39th minute.
Patrice Evra's pass through the middle was teed up for Scholes by Louis Saha and the United midfield man scored with a fierce shot from 25 yards.
United made it 2-0 one minute after the break.
Darren Fletcher drove his corner to the back of the Copenhagen box where defender John O'Shea stuck out an involuntary right leg to guide the ball past goalkeeper Jesper Christiansen.
Until then it was Christiansen who was responsible for keeping the score down.
Christiansen, who had enjoyed an excellent game, made his only mistake seven minutes from time when he badly fumbled Kieran Richardson's 25-yard left-foot shot for United's third goal.
Until then, Christiansen had made a series of fine saves.
He produced the first within the first minute blocking Saha's shot from the edge of the box after the Frenchman had been put through by a Wayne Rooney pass.
In the 33rd minute, Evra's ball out of the United box found Rooney whose glorious through ball set Saha free on the edge of the Copenhagen penalty area.
Saha's shot was well blocked by Christiansen, although the ball almost rolled on through his legs and into the net.
Christiansen produced another fine effort to claw away Michael Carrick's 20-yard drive after 35 minutes, but his best save of the game came soon after when he clipped away Cristiano Ronaldo's close-range header at full-stretch.
After his mistake, the Copenhagen goalkeeper still produced two fine late stops to deny United's substitutes Alan Smith and Ole Gunnar Solskjaer.
Although United were always in control, the Danes did have their chances to score but found Edwin Van der Sar in excellent form.
The United goalkeeper made superb saves to keep out two fierce 25-yard shots from Michael Silberbauer midway through the first half.
But his best effort was an acrobatic effort as he flew through the air to turn away Atiba Hutchinson's blistering 20-yard shot in the 65th minute.