A second-half goal from Kanu was enough to send Portsmouth through to their first FA Cup final in 69 years.
Ex-West Brom striker Kanu side-footed an easy chance to see off the Baggies after Dean Kiely had denied Milan Baros and Zoltan Gera had failed to clear.
Baros, who looked to have handled in the build-up to the goal, missed a simple chance to seal the win.
They were almost made to pay but Robert Koren's shot hit the bar and Ishmael Miller fired wide late on.
Portsmouth will face the winners of the all-Championship tie between Barnsley and Cardiff on Sunday in the final.
Their win carries on the top flight's run of having a team in every FA Cup final.
Pompey were already odds-on favourites to lift the trophy before the game, but for long periods it was West Brom who looked the better bet for a return to Wembley on 17 May.
Harry Redknapp's south coast side were not at the races during a lacklustre first-half display and it Albion who looked like the Premier League thoroughbreds.
606: DEBATE
Portsmouth's defensive pair of Sol Campbell and Sylvain Distin struggled throughout to deal with veteran forward Kevin Phillips dropping deep.
The former Southampton striker found plenty of space and tested Pompey early on with a long-range shot just over the bar before a neat lay-off that ended with Zoltan Gera causing problems for a fumbling David James with a low shot.
Portsmouth were all at sea going forward, with Baros wasteful and Kanu barely contributing as Redknapp looking increasingly agitated on the sidelines.
They enjoyed their best spell of the first half shortly before the break but Redknapp, on his first appearance in the FA Cup semi-finals and at Wembley as player or manager, would have had strong words at the interval.
There appeared to be little immediate change in Pompey's play, but less than 10 minutes after the break they broke the deadlock.
Glen Johnson played a ball into Baros, who may have controlled the ball with his arm before getting off a shot which Kiely did well to keep out.
However, as Kiely looked to pounce on the loose ball Gera tried to clear and could only steer the ball into the direction of Kanu to slot into the empty net from only a couple of yards out.
It should have been game over as Baros was played in by a slide rule pass from Niko Kranjcar and seemed certain to score, but he made an awful hash of the finish and Kiely produced a desperate save.
The Baggies almost made them pay as the game burst into life in the latter stages.
Carl Hoefkens set up Koren and his shot beat James but smacked the top of the bar.
Moments later substitute Miller got clear on the left and tried to pick out Phillips at the back post, but James anticipated well and plucked his cross out of the air.
There were further worries as Hoefkens set up an onrushing Miller but he side-footed wide and Pompey survived to book their place in the final.
West Brom: Kiely, Hoefkens, Albrechtsen, Clement, Robinson, Morrison (Brunt 60), Koren, Gera (Kim 75), Greening, Bednar (Miller 60), Phillips. Subs Not Used: Danek, Pele.
Portsmouth: James, Johnson, Campbell, Distin, Hreidarsson, Diarra, Diop, Muntari, Kranjcar, Kanu (Davis 80), Baros (Nugent 71). Subs Not Used: Ashdown, Lauren, Pedro Mendes.
Booked: Baros.
Goals: Kanu 54.
Att: 83,584
Ref: Howard Webb (England).
BBC Sport Player Rater man of the match: Niko Kranjcar (6.70 on 90 minutes).
Player Rater
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