Kanu's tap-in goal and a clinical defensive performance in the second half swept Portsmouth into their first FA Cup final since 1939 and wrecked hopes of a first all-Championship showdown.
Kanu, twice an FA Cup winner with Arsenal, continued his love affair with the competition with a simple finish in the 55th minute after former Pompey goalkeeper Dean Kiely could only push out Milan Baros' shot.
Baros had other chances to wrap it up but with Sol Campbell and Sylvain Distin rock solid in defence, David James was barely troubled despite a late West Brom rally in which Robert Koren hit the top of the crossbar.
Pompey arrived for their first Wembley appearance in 69 years with a record of seven wins in their previous nine games and lying sixth in the Barclays Premier League.
Apart from cup-tied striker Jermain Defoe, all their top players were in place but for a long time you could not tell them apart in terms of quality from promotion-chasing Albion, playing their fourth semi-final since winning the FA Cup in 1968.
The occasion seemed to overwhelm both sides for too long but Kanu's scrambled goal 10 minutes into the second half gave them enough inspiration to go through.
Albion, spearheaded by prolific veteran ex-Saint Kevin Phillips, who has 24 goals this season and five in the previous seven games, were first to fire as Pompey made a stuttering start.
Phillips clipped a shot over James' crossbar from 20 yards and in the sixth minute England goalkeeper James spilled a tame effort by Gera and was thankful to see Campbell clearing up the loose ball.
Albion continued to dictate the pace, although Hermann Hreidarsson, passed fit before the kick-off after an Achilles injury, almost sent Baros clean through the inside left channel, his pass just a shade heavy.
It took nearly 30 minutes for Pompey to raise their first shot on target, and that an optimistic 35-yard free-kick by Muntari which went straight down Kiely's throat.
Baros' frustrating first half was epitomised when he shrugged off Martin Albrechtsen and fired over from the edge of the area, only to be booked by referee Howard Webb who had already whistled for a foul.
James caused Pompey another flutter trying to keep Johnson's back-header from going out for a corner, palming it straight back towards the lurking Phillips but recovering just in time.
But Pompey were at last beginning to exert some pressure towards half time and Muntari got much closer for a strike after a determined solo run and drilled his shot just off target.
Redknapp resisted the temptation to make changes at the interval and the decision was justified when Pompey nosed ahead with a streaky goal in the 55th minute.
The ball finally ran for Baros following a free-kick which was turned back into the area by Glen Johnson and the Czech striker's shot was palmed out by Kiely.
The keeper scrambled across his line to get another despairing touch but Zoltan Gera inadvertently got in the way and the ball rebounded to Kanu who had the easiest job in the world to tap home.
Albion boss Tony Mowbray called for a double substitution on the hour. He had started with Czech Roman Bednar supporting Phillips up front but sent on Chris Brunt and quarter-final hat-trick hero Ishmael Miller for Bednar and midfielder James Morrison.
But Pompey were looking a different side now, full of running and Baros should have made it 2-0 on 65 minutes.
Kiely had already had to charge out of his area to stop him collecting a long, through ball but the striker - still to score during his loan spell with Pompey from Lyon - should have left him helpless from a Kranjcar pass.
Kiely deserved big credit for blocking Baros' hesitant shot.
Baros left the action with 20 minutes left to be replaced by David Nugent but it was West Brom who threatened next, Koren's snap-shot clipping the bar in the 73rd minute.
Muntari was just wide with a cross-shot and Nugent had the chance to seal it but failed to beat the brave Kiely and Pompey were finally able to breathe more easily after Miller's shot from a Carl Hoefkens cross passed inches wide with six minutes left.
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