The surprise win took Portsmouth back to Wembley, for the first time since 1942, for the semi-finals and ended United's hopes of repeating their 1999 treble triumph.
For Redknapp, who has previously knocked United out of the FA Cup with both Bournemouth and West Ham, it was another victory over Sir Alex Ferguson to savour.
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 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 defender Sol Campbell.
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 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 subsequent shot snaked just inches wide.
United were taking control, and Evra should have done better than cross behind Tevez after being sent 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, with James stretching 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.
Kranjcar broke down the right and played in substitute Baros, who was felled by Kuszczak.
The Pole 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 the penalty with the minimum of fuss.
Man Utd: Van der Sar (Kuszczak 46), Brown, Ferdinand, Vidic, Evra, Ronaldo, Scholes, Hargreaves (Carrick 68), Nani, Rooney, Tevez (Anderson 68). Subs Not Used: O'Shea, Park.
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