Then, in the 76th minute, the visitors broke from their defensive shackles as goalkeeper David James launched a long kick out of defence.
United's Anderson was beaten to the ball by Milan Baros and it fell kindly to Niko Kranjcar out on the right. His return pass sent Baros racing clear through the middle.
As the Czech Republic international tried to round United's substitute goalkeeper, Tomasz Kuszczak, he was brought down by the Pole.
Referee Martin Atkinson pointed to the penalty spot and brandished the red card in Kusczak's direction, although Wayne Rooney was almost behind his goalkeeper as the last line of defence.
Rio Ferdinand went in goal, but he was powerless as Muntari stepped up to coolly drill in his left-foot spot-kick beyond the England defender and into the bottom right corner of the net.
Ironically, Kuszczak had been on the field for just over half an hour after replacing the injured Edwin Van der Sar at half-time.
It was Pompey's first win at Old Trafford for over 50 years and ended United's hopes of a treble. Yet they had to ride a United storm and had some huge slices of luck on their way to the semi-finals.
United could have had a penalty of their own in the seventh minute.
A super crossfield pass by Rooney saw Cristiano Ronaldo take the ball down in one and then skin Pompey full-back Hermann Hreidarsson as he raced into the box from the right wing.
But near the byline, Ronaldo was blocked off by Sylvain Distin and the Portuguese winger looked round in horror to see Mr Atkinson waving play on.
Pompey had another escape in the 19th minute after Wes Brown released Carlos Tevez down the right.
His ball inside sent Rooney racing clear through the middle and, just as the England man seemed set to fire beyond James from the edge of the box, Sol Campbell's brilliant intervention stopped the United striker in his tracks.
The ball fell to Tevez, whose shot from the edge of the penalty area was headed off the line by Glen Johnson.
United continued to attack, but they found James and his defenders a massive obstacle to their ambitions.
When Ronaldo's back flick on the edge of the Pompey box left Michael Carrick free with only James to beat, he was held up by the England goalkeeper and then denied on the goal-line by a magnificent Distin block.
Three minutes later Patrice Evra's blistering shot from the left edge of the Pompey penalty area was superbly tipped on to the post by James.
United may have had the star players in their pack, but it was Pompey's defenders who eventually held all the aces.