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.
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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."
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.
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.
Portsmouth rode their luck once more 10 minutes later when James pushed Drogba's 30-metre free kick against the bar.
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.
