A Cristiano Ronaldo header early in the second half underlined their superiority and although Miles Addison reduced the arrears, Danny Welbeck had the final word for Sir Alex Ferguson's side.
It was unlikely that Derby could ambush United as they had done in the first leg of the Carling semi-final and it was clear the visitors were in no mood for another slip-up as they sliced open the home defence almost at will.
Darren Fletcher and Ji-Sung Park were both denied by the reflexes of Stephen Bywater and it was no surprise when United finally went ahead in the 29th minute.
Giggs swept the ball out to Nani and the winger cut in from the left before bending a right-foot shot inside Bywater's left-hand post.
United thought they had scored again when Ronaldo ran clear in the 37th minute but a late linesman's flag cut short the celebrations, although a second goal was not far away.
When a Ronaldo free-kick bounced off the wall, Gibson drove a first-time shot into the bottom corner and Derby must have sensed they were on their way out.
The contest was finished three minutes after the interval when Ronaldo lost his marker to head in a Giggs corner from ten yards.
At least Derby kept plugging away and Addison headed in a Kris Commons cross in the 56th minute to give the home fans a glimmer of hope.
Then Ben Foster was forced into his first meaningful save in the 77th minute to keep out a Gary Teale shot, but Giggs and Fletcher combined nine minutes from the end to set up Welbeck for a beautifully executed finish.
That emphasized the gulf in class between the teams.