In what was a lively start to the game, there was an early shout for a penalty when winger Chem Campbell turned inside full-back Bali Mumba and had his shirt pulled, but the referee waved away the appeals.
The biggest chance of the half came after 15 minutes when a Dexter Lembikisa cross was pulled back to Lee Harkin 10 yards out, but his good effort was saved by goalkeeper Joe Rose.
Wolves were getting joy down both flanks and this time Hugo Bueno lifted a cross in from the left, which Campbell glanced wide.
Wolves’ pressure finally told just before the half-hour mark when Bueno followed up his Premier League Cup final goal with another excellent strike. A one-two between Bueno and Luke Cundle saw the left-wing-back arrive on the edge of the box and a wonderful right-footed shot curled into the far corner.
A dominant first half display saw Wolves enter the break deservedly leading 1-0, with a place in the play-off final in their hands.
The start of the second half was more competitive but Wolves still created the first chance, when Harkin’s header flashed just wide of the post.
Norwich offered a warning sign when Abu Kamara broke free at the back post and had a free header, but he was only able to direct it straight into the hands of goalkeeper Matija Sarkic.
Wolves should have extended their lead when some delightful skill from Taylor Perry saw him get out of a tight situation by the corner flag and race towards the Norwich goal. His low cross found Harkin who smashed his effort off the post.
The woodwork again came to Norwich’s rescue moments later when Campbell hit the underside of the crossbar with a powerful effort. A superb Joe Hodge pass put the winger through.
But after failing to capitalise on their chances, Wolves were pegged back when Tyrese Omotoye scored Norwich’s equaliser. The substitute latched onto a loose ball and curled home a very similar goal to Bueno’s from the first half.
Campbell had a chance to win it in added time when he was played through on goal but he hit it straight at the goalkeeper, before Christian Marques directed a free header wide with the last kick of the game before extra-time.
Tired legs took their toll in what was an uneventful 30 minutes of extra-time, as penalties were needed to separate the teams.
There were eight excellent penalties to start as every player scored, until Flynn Clarke had his spot kick saved by Sarkic. Local lad Ollie Tipton had a chance to win it with Wolves’ final penalty and the centre-back sent Rose the wrong way to seal a place in the final.
Wolves will enjoy home advantage once more in the final when they face Stoke, who beat Nottingham Forest 2-0 in their semi-final. No date has been announced for that game yet.
Wolves: Sarkic, Tipton, Marques, Hubner, Lembikisa (Birtwistle, 108), Cundle, Hodge (Hesketh, 91), Perry, Bueno, Campbell, Harkin (Griffiths, 75).
Subs not used: Kandola, Shabani.
Norwich: Rose, Earley, Tomkinson, Shipley, Mumba, Gibbs, Springett, Adshead (Khumbeni, 110), Rowe, Kamara (Omotoye, 58), Dickson-Peters (Clarke, 81).
Subs not used: Berry, Giurgi.