Portuguese winger Nani gave United the lead in the 29th minute before Darron Gibson doubled their advantage on the stroke of halftime.

World Player of the Year Cristiano Ronaldo added the third four minutes after the restart.

Miles Addison pulled one back for Derby but Danny Welbeck killed off their hopes with an 81st-minute goal.

United, who also eliminated Derby from the League Cup semi-final, will face either Swansea City or Fulham in the last eight.

Everton also secured passage to the quarter-final after defeating Aston Villa 3-1 at Goodison Park.