Didier Drogba got the winner with a 59th minute free-kick after they hit the woodwork five times in the first half and Frank Lampard missed a late penalty.
In an astonishing match of twists and turns, Kevin-Prince Boateng, who scored from the spot in the semi-final at Wembley, also saw his 56th minute penalty saved.
The triumph gave the west London side a second straight FA Cup final victory, after they beat Everton last season, and their third success in four seasons.
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Although the newly-crowned Premier League champions dominated relegated Portsmouth in the opening half, they were thwarted on five occasions when Drogba (twice), Frank Lampard, Salomon Kalou and John Terry all hit the bar or post.
Despite that Portsmouth's incredibly vociferous fans made the greater noise inside the sun-drenched stadium and stayed to applaud their side even after defeat.
Chelsea manager Carlo Ancelotti, who has won the Double in his first season in England, told reporters afterwards: "Its a fantastic victory for me, I am very happy.
"We won't do anything special to celebrate, I will follow my players and my friends. Wine, sure, champagne. It is right to have a celebration, the team had a fantastic season."
"It has never happened in my career to hit the bar or post five times in one half... and we didn't start too well in the second half but I was not worried because we were in control of the game and had chances to score."
Portsmouth manager Avram Grant said: "It was a very difficult season. It is a season I will not forget. I have won a lot of games in my life, trophies and everything, but this was unbelievable. We always played against the odds."
OVERWHELMING FAVOURITES
Chelsea began as 5-1 on favourites to beat Portsmouth who are in administration, have debts of 138 million pounds and finished bottom of the Premier League.
Some pundits had predicted a record FA Cup final victory following Chelsea's 8-0 trouncing of Wigan Athletic when they clinched the league title at Stamford Bridge last Sunday.
But Portsmouth, many of whose players might have been playing their last match for the club because of the financial problems and relegation, weathered the storm.
In contrast Chelsea had just one first half scare with Cech producing an outstanding reflex save to deny Frederic Piquionne.
Pompey's first close shave came after 14 minutes when Lampard shot against the outside of David James's left-hand post with a 25-metre drive.
Kalou was guilty of one of the most blatant misses in any Cup final after 27 minutes when he shinned an Ashley Cole cross against the bar in front of an open goal from four metres.
A minute later Chelsea captain Terry headed the ball against the bar again with the under-fire James beaten.
Portsmouth rode their luck once more 10 minutes later when James pushed Drogba's 30-metre free kick against the bar.
UTTER FRUSTRATION
The right-hand post came to Portsmouth's rescue again two minutes later when Drogba cracked the ball against it from close range with England goalkeeper James again beaten.
The Ivory Coast striker, who will lead his country at the World Cup finals, showed his utter frustration by smac
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