The holders will play Aston Villa in the final after overturning a 2-1 deficit from last week's semi-final first leg.
Goals from Paul Scholes and Michael Carrick had put United in charge but the tie appeared destined for extra-time after Carlos Tevez pulled one back for City.
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Rooney, however, had the final word with the England striker scoring his 21st goal of the season to send Sir Alex Ferguson's side back to Wembley.
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