City had taken a 2-1 lead from the first leg, and a tense first half ended nil-nil before Paul Scholes put United back into the tie.
Michael Carrick scored in the 71st minute before Carlos Tevez, the United old boy sent visiting fans into raptures by equalising the aggregate scoreline.
With extra time looming, Wayne Rooney headed home an injury time winner to take the match beyond doubt, and win the semi-final by four goals to three on aggregate.
City will have to wait for another chance to deprice their red neighbours of a trophy, but their fans must surely take heart from just how close they ran their long-time superiors in 180 minutes of gripping football.
Even United fans must agree that a strong Manchester City side adds a huge amount of intrigue to what has always been a heated rivalry. So, while United head to Wembley and take the bragging rights this time, it must surely be the first of many high profile big matches between these sides in the modern era.
United are rewarded with a Carling Cup final against Martin O’Neil’s Aston Villa who defeated Blackburn Rovers in their semi-final.
