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.
Phillips was a threat from the start
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.
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