Jonny Howson had swept the Canaries, who finished the regular season in third place, ahead on 41 minutes, after goalkeeper John Ruddy earlier produced a fine double save and Norwich midfielder Alex Tettey hit the post.
Ipswich, though, dragged themselves level in first half stoppage time through substitute Paul Anderson, who came on after midfielder Luke Varney had been taken off on a stretcher with what looked like a serious lower leg injury.
Both sides failed to create any real openings in what was a largely cagey second half, and will now battle it out at Carrow Road next Saturday for a place at Wembley.
After soaking up some early pressure from the home side, Norwich - who left Suffolk with a 1-0 league victory back in August - created some space down the right through Bradley Johnson, but Graham Dorrans failed to make a clean connection as the ball dropped at the far post.
On eight minutes, Ipswich were denied by a superb double save from Ruddy.
Daryl Murphy picked up on a loose clearance from Norwich captain Russell Martin and powered into the right side of the penalty area.
His cut-back was met by Freddie Sears, but Ruddy was well placed to make a smart reaction block with his legs before getting up to deny Varney's header, with full-back Steven Whittaker nodding the rebound off the line at the far post.
At the other end, Ipswich defender Luke Chambers did well to get in front of Howson as the midfielder looked to head Whittaker's cross goalwards, the ball bouncing back off the Norwich man and behind.
Norway international Tettey was within inches of putting the Canaries ahead on 21 minutes when his 20-yard curling effort hit the outside of Bartosz Bialkowski's left-hand post.
Ipswich were forced into a change when Varney was injured after an awkward fall and had to be taken off on a stretcher
Ipswich's official Twitter account said it was a possible Achilles injury and he would undergo a scan
Following a lengthy stoppage, Anderson replaced him and play resumed on 30 minutes.
The hosts used the interruption to regroup, and Murphy glanced a header across the face of goal.
Norwich, though, swept into the lead on 41 minutes.
Cameron Jerome barged through Tommy Smith for a ball on the left, with referee Anthony Taylor waving play on.
The Canaries forward strode away down the flank, before cutting the ball back across goal for Howson to arrive on queue and tuck it confidently into the bottom right corner, sparking wild celebrations from the Norwich bench and some 2,000 away fans squeezed into the far end of the Cobbold Stand.
Ipswich, though, were level three minutes into the six of stoppage time.
Martin's header dropped to Sears at the edge of the penalty area, who drilled in a low angled shot, which Ruddy spilled and then kicked away.
However, Anderson was first to the rebound, lashing the loose ball past the three yellow shirts on the line and this time all four sides of Portman Road erupted.
Dorrans was booked at the start of the second half for hacking down Anderson as he looked to get away on the left, before on 57 minutes Jerome followed him into the referee's notebook after a trip from behind on Christophe Berra.
Bialkowski got down quickly to hold on to Johnson's low 18-yard effort while at the other end, a deep ball into the Norwich box from the right was headed over by Sears.
On 68 minutes, Chambers deflected Johnson's angled drive wide.
The match them became somewhat scrappy as both sides struggled for sustained periods of possession.
Norwich, who had just missed out on automatic promotion by three points, sent on Gary Hooper for the closing five minutes, the former Celtic frontman replacing Jerome.
Nathan Redmond's looping header was tipped over, but there was to be no grandstand finale.
Source : PA
Source: PA