Sulley Muntari scored the winner from the spot with 12 minutes left after Milan Baros was upended by United's substitute keeper Tomasz Kuszczak.
Kuszczak, who replaced Edwin van der Sar at half-time, was sent off and Rio Ferdinand was beaten from the spot.
Pompey survived a siege, with Sylvain Distin denying Michael Carrick on the line and Patrice Evra hitting a post.
It took Portsmouth back to Wembley for the first time since 1939 for the semi-final and ended United's hopes of repeating the treble the won in 1999.
And for Redknapp, who has previosuly knocked United out of the FA Cup with Bournemouth and West Ham, it was a day of triumph.
Paul Scholes, Carlos Tevez and Owen Hargreaves all returned to United's starting line-up after the Champions League victory over Lyon - and they met with stubborn and well-organised Portsmouth resistance.
United were understandably furious after six minutes when Cristiano Ronaldo was clearly bundled over by Distin as he raced into the area, but referee Martin Atkinson ignored the appeals, to the clear disgust of Sir Alex Ferguson.
Pompey rarely threatened, but United keeper Van der Sar was in some discomfort as he scrambled to save a long-range shot from Niko Kranjcar.
United missed a glorious chance to break the deadlock after 18 minutes when Tevez and Wayne Rooney led a counter-attack, but the England striker was blocked by keeper David James.
The rebound fell for Tevez, but Glen Johnson made a superb recovery to block his goal-bound effort on the line.
James had been well-protected by his defence, but he needed to be sharp to drop to his right and save a low drive from Tevez.
It had been a very satisfactory first half for Portsmouth, but United had a problem in the interval when keeper Van der Sar withdrew through injury and was replaced by Kuszczak.
Pompey almost came unstuck in a goalmouth scramble after 57 minutes, when Tevez was blocked by defenders on the line and Ronaldo's shot snaked just inches wide.
United were taking control, and Evra should have done better than cross behind Tevez after being put clear into the area by Rooney.
Ferguson made a double change after 67 minutes, sending on Anderson and Carrick for Tevez and Hargreaves.
And Carrick was the central figure in a remarkable escape for Portsmouth three minutes later.
Ronaldo's brilliant back-heel played him into area and a goal looked certain as he rounded James, but Distin made a miraculous recovery to make the clearance.
United were turning up the heat, and James then stretched to make a superb save from Evra, turning his shot on to the post.
After surviving a second-half siege, Portsmouth broke out to take the lead in remarkable circumstances with 12 minutes left.
Kranjcar broke down the right and played in substitute Baros, who was felled by Kuszczak. He was shown the red card by referee Atkinson despite the fact that Rooney and Anderson were patrolling the goal-line.
Ferdinand went in goal as replacement, but he stood no chance as Muntari drilled home home the penalty with the minimum of fuss.