Ipswich went down 4-2 on aggregate having had Christophe Berra sent off four minutes into the second half for handling Nathan Redmond's goalbound shot, with Wes Hoolahan scoring the resulting penalty to put Norwich ahead in the tie.
The visitors levelled on the hour when Tommy Smith reacted quickest to Daryl Murphy's header to stab the ball home but celebrations lasted four minutes as Redmond rifled a low shot past keeper Bartosz Bialkowski to restore Norwich's lead.
The home side sealed victory over their local rivals, and a place in the May 25 final, 13 minutes from time when Cameron Jerome converted Redmond's astute pass.
With the winners of the final set to earn an estimated 120 million pounds ($188.72 million) by reaching the Premier League, Ipswich manager Mick McCarthy had a sobering message for fans of the two clubs involved.
"I've seen Middlesbrough cock-a-hoop on the pitch last night and the same with Norwich today. One of them is going to be as sick as a seaside donkey, just like I feel now...they've got to win it," said McCarthy.
"Even if we'd have won today and lost at Wembley I'd have still felt sick."
Bournemouth and Watford have been automatically promoted to the top flight.
(Writing by Justin Palmer, editing by Ken Ferris)
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