Portsmouth stumbled into the FA Cup Final as former West Brom striker Kanu returned to haunt his old club with the only goal of the game nine minutes into the second half.
The favourites, seeking to avert the threat of the first all-Championship Final in the history of the competition, were largely outplayed in the first half.
But Harry Redknapp, bidding to win his first major trophy in the game, addressed the shortcomings of his side in the dressing-room at the break and after the lanky Nigerian marksman found the net better finishing would have led to a more emphatic scoreline.
Redknapp said: "We haven't won anything yet but we are never going to get a better chance to win the FA Cup.
"We were favourites coming into the semi-final and we will be favourites in the Final itself.
"We are a decent side, a top 10 Premier League side and if we play as I know we can play we will be all right."
Yet Redknapp was the first to admit that West Brom caused his side problems, particularly in the first half.
"They did, without a doubt. We had to change things round at halftime because they were seeing far too much of the ball.
"But once we sorted ourselves out I never really thought were in danger of losing once we went in front.
"Sure we could have done with a second goal and we had enough chances to get it, but I always knew it would take something special to beat David James."
Scorer Kanu said: "It was nice to get the goal but it was difficult to miss!
"I've won the Cup before with Arsenal, but it will be a different kind of achievement if I do it with Portsmouth because nobody gave us any hope."
West Brom coach Tony Mowbray was naturally disappointed, but with six games remaining in the Championship to ensure promotion he concedes there are more pressing matters than a return trip to Wembley for the Final.
Mowbray said: "On the balance of play and chances created I felt we held our own and there was nothing in it. But our priority is the league - and we have six more cup finals coming up!"
The Baggies certainly started brightly against the favourites and sole Premier League survivors.
Sustained pressure saw Pompey pegged back in their own half and Zoltan Gera's stinging drive from the edge of the penalty area almost proved too hot to handle for England keeper James, who gathered at the second attempt.
Portsmouth were struggling against their energetic opponents. And with almost 30 minutes of play gone the Premier League side's sole attempt on goal was a rather optimistic 35-yard free-kick by Sulley Muntari that never looked like troubling their former keeper Dean Kiely.
While Kevin Phillips appeared to well kept in check by Sylvain Distin, the duel between Milan Baros and Paul Robinson was bordering on boiling over.
And the former Liverpool striker had to tread carefully after needlessly being booked on 36 minutes for playing on after referee Howard Webb had blown to halt play.
Yet, in a game that was fast turning into a typically tense and disappointing semi-final, it was Baros who almost put Pompey in front minutes before the break when he latched on to Kanu's clever through-ball.
Unfortunately for the top-flight side the ball evaded the Czech international's outstretched leg, enabling Kiely to race from his line and collect.
The interval didn't bring much of a change until Portsmouth broke in numbers in the 54th minute and finally got their noses in front.
Glen Johnson's diagonal ball sent Baros away and when his initial shot was saved by Kiely, Kanu followed up to score from close range.
Ten minutes later Baros should have put the game beyond the reach of the Championship side but faced by just Kiely he stumbled in front of goal and his partially hit shot was easy pickings for the West Brom keeper.
The game began to open up and after Robert Koren's 20-yard drive smashed against the Pompey bar chances came and went at either end.
Baggies sub Ishmael Miller missed two gilt-edged opportunities to level matters while Pompey's Nico Kranjcar and David Nugent were equally inept in front of goal in the closing stages.
STAT ATTACK
STORY OF THE GAME
WEST BROM PORTS'TH
62% POSSESSION 38%
0 SHOTS ON TARGET 6
6 SHOTS OFF TARGET 4
2 CORNERS 2
12 FOULS CONCEDED 21
4 OFFSIDES 7
0 YELLOW CARDS 1
0 RED CARDS 0
HOW THEY RATED
WEST BROM
Kiely 7, Hoefkens 6, Albrechtsen 7, Clement 7, Robinson 6, Morrison 7 (Brunt 6), Koren 6, Gera 7 (Kim 7), Greening 6, Bednar 6 (Miller 7), Phillips 7.
Manager Mowbray 7
PORTSMOUTH
James 7, Johnson 6, Campbell 7, Distin 7, Hreidarsson 7, Diarra 7, Diop 6, Muntari 7, Kranjcar 6, KANU 8 (Davis 6), Baros 7 (Nugent 5).
Manager Redknapp 7
Referee H Webb 6
HEAD TO HEAD
Jonathan Greening v LASSANA DIARRA
The Frenchman's class told throughout as he dictated the play in midfield and nullified the threat of Greening.
MAN OF THE MATCH
KANU
Inflicted heartache on his former club by grabbing the only goal to ensure the favourites didn't become victims of another shock in this season of Cup upsets.