Frederic Piquionne, who is on loan from Lyon, broke the deadlock in the ninth minute of extra time. Former Spurs midfielder Kevin-Prince Boateng added another from the penalty spot 18 minutes later.
"This season encapsulates just about every emotion you can have as a footballer and today has been absolutely superb," said goalkeeper David James, who was the only remaining player in Sunday's starting lineup from the 2008 team that won the cup.
Portsmouth manager Avram Grant will come up against former side Chelsea in the May 15 final after the defending champions beat Aston Villa 3-0 on Saturday.
It will be a remarkable conclusion to a season for Portsmouth, which became the first Premier League team to go into financial administration last month and has court-appointed insolvency experts running the club while trying to find a buyer.
Winning the semifinal will provide about $3 million in prize money and ticketing revenue for the south-coast club, which is still in bankruptcy protection.
"This is a great achievement after what's happened this season," Grant said. "I remember arriving at the club one day (in February) and being told that next week there will be no club. We have been living on a day-(to)-day basis and despite this we have reached the final."
Portsmouth did that by overcoming a Spurs side manged by Harry Redknapp, who led it to glory on the same pitch two years ago. But winning its first trophy since 1950 came after overspending on player transfer and salaries.
Drastically cutting the squad in the ensuing financial meltdown couldn't prevent Portsmouth from entering financial administration and receiving a nine-point deduction.
Relegation to the League Championship was confirmed Saturday after West Ham's victory over Sunderland ended any faint hopes of survival.
Tottenham profited most from Portsmouth's plight, signing Redknapp in 2008 and numerous players, including strikers Jermain Defoe and Peter Crouch.
Neither striker, though, provided much threat for Spurs, who are fifth in the league and in the running for a Champions League spot, against their last-place opponents.
"Pompey were dangerous on the counterattack. They had pace," Redknapp said. "They are a threat and full credit to them. We had plenty of chances, good chances, but missed them and that's how it goes."
Tottenham's best chance in the first half came when Crouch rose above Ricardo Rocha, but his header was blocked by a diving save from James.
Rocha and Aaron Mokoena were solid in defense for Portsmouth, with Piquionne dangerous up front. The striker's best chance in the first half came after being released by Hassan Yebda, but his shot was blocked by goalkeeper Heurelho Gomes' outstretched leg.
Spurs came out fighting at the start of the second half and dominated without troubling James too much.
Defoe soon had a shot that was partially blocked by Rocha and a weak shot in the in the 57th was his last contribution before the England striker was replaced by Roman Pavlyuchenko.
Spurs had a penalty claim dismissed on the hour when Portsmouth defender Steve Finnan handled Gareth Bale's cross, while Crouch missed the target with several headers to allow Portsmouth to cling on and send the game into extra time.
And it was the soggy Wembley pitch that helped to settle a game lacking much quality.
Boateng flicked on Mark Wilson's free kick and, as Spurs centre back Michael Dawson slipped, Piquionne slotted the ball under Gomes.
"How can you play on a pitch you can't stand up on?" Redknapp said. "It's farcical."
Spurs thought they had immediately equalised when Crouch turned Bale's cross into the net, but referee Alan Wiley ruled that James had been fouled.
"We scored a good goal that was disallowed, having now watched it a few times. But that's how it goes," Redknapp said.
Corluka missed another opportunity to equalise in the 25th minute of stoppage time, and then Wilson Palacios conceded a penalty by fouling Aruna Dindane. Boateng fired the spot kick into the net to ensure his team will be returning to Wembley next month.
