A tie tantalisingly poised at 1-1 after the first leg sprung into life in the 49th minute when Wes Hoolahan converted a penalty after Ipswich defender Christophe Berra was sent off for handling Nathan Redmond’s effort on the line.
Ipswich pulled themselves level on the hour mark when Tommy Smith bundled home from close range, before Redmond restored Norwich’s advantage four minutes later with a low strike from inside the area.
And Cameron Jerome poked in a third for the hosts in the 76th minute as Alex Neil’s side secured a place against Middlesbrough in next Monday’s Wembley final.
Both sides made one change from last Saturday’s draw at Portman Road, with Graham Dorrans dropping to the home bench in favour of Hoolahan and Paul Anderson starting for Ipswich in place of the injured Luke Varney in a crucial 99th East Anglia derby.
Neither keeper was tested during a cagey first half at a sell-out Carrow Road, where the visitors constantly pressed to give Norwich minimal time and space in possession.
The hosts almost opened the scoring on 16 minutes when Russell Martin drilled a low strike through a congested area, but Anderson, scorer of Town’s equaliser in last week’s first leg, cleared off the line with Bart Bialkowski beaten.
Ipswich’s best chance of the half came when Anderson dispossessed Martin on the edge of the home area and saw his cross find Kevin Bru, but the Mauritian blazed his first-time effort over the bar.
Hoolahan made space on the left and broke clear of Tommy Smith to feed in Jonny Howson late on in the half, but the winger saw his effort blocked by the legs of Tyrone Mings.
With the second half starting at a much faster tempo, Hoolahan broke away to find Redmond, who cut inside on to his right foot before seeing his curling effort blocked on the line by the arm of Berra. After referee Roger East dismissed the Scottish centre-half, Hoolahan coolly sent Bialkowski the wrong way from the spot to give the hosts the lead.
Despite the man disadvantage, Town pulled themselves when a long free-kick in to the area was flicked on by Daryl Murphy. Smith reacted quickest to turn the ball home, racing the length of the pitch to celebrate with the travelling supporters.
Four minutes later, Martin Olsson’s effort from an acute angle was smothered by Bialkowski but the ball found its way to Howson, who side-footed for Redmond to drill in to the corner to restore Norwich’s lead.
With gaps starting to appear in the visitors’ defence, Hoolahan’s fierce strike was well held by Bialkowski and Bradley Johnson’s effort was blocked by a last-ditch Mings challenge.
Jerome then somehow failed to turn in Howson’s cross from no more than six yards out, but made amends a few minutes later by toe-poking home from inside the area to seal Norwich’s victory, leaving Neil’s men one game from a return to the Premier League.