Drogba's 37th goal of the season was a free-kick just before the hour that found the net with tracer-bullet precision from 20 yards.
It maintained Drogba's impressive record of scoring in all six competitive games he has played at the new Wembley and confirmed Chelsea as only the seventh club to complete the league and FA Cup double, a pretty significant achievement in Carlo Ancelotti's first season in charge.
But that does not even come close to telling the story of a game that saw Chelsea hit the woodwork five times before the interval, including a terrible miss from Salomon Kalou, Kevin-Prince Boateng fail to convert a penalty shortly before Drogba's winner that could have set up a fairytale finish to a shambolic season of turmoil at Portsmouth, and even Frank Lampard fired wide from the spot three minutes from time.
Given the financial straightjacket they find themselves in, this was likely to be Pompey's last major final for quite some time.
That certainty, at the end of a campaign where you are 135 million pounds in debt, in administration, have had nine points deducted, been relegated, not been paid your wages on time on numerous occasions and seen players sold at a moment's notice, probably generated a devil-may-care attitude within the Portsmouth squad.
Frederic Piquionne brought a staggering reaction save out of Petr Cech during the first half and Aruna Dindane failed to make clean contact as he tried to turn home Piquionne's cut-back a few minutes later.
By any standards, these were glorious openings which Portsmouth might have had cause to regret if it were not for the fact that Chelsea were enduring such great frustrations of their own that Drogba ended the half slapping a post in total irritation at his side's inability to get the ball past it.
Within this flurry of activity came a contender for the best save ever seen in a cup final, and that miss.
Chelsea's victory will save Kalou extreme ridicule, but he knows his own contribution is going to be replayed so often he will never escape.
Frank Lampard had already flashed a 14th-minute shot against a post and Chelsea were on top when Ashley Cole, the first man to win the famous old trophy six times, drove deep into the Pompey box, completely outpacing Aaron Mokoena.
Fabio Capello would not have been the only one to admire his sublime cross, which completely took David James out of the game and presented Kalou with a four-yard tap-in.
The Chelsea fans were already on their feet, arms aloft in triumph, when Kalou's shinned effort soared skywards and thudded against the bar.
For a moment or two, the stadium was completely silent, as if unable to comprehend what it had just witnessed. The eruption of noise from the Portsmouth end confirmed the reality.
Within a couple of minutes, John Terry had glided a header against the bar, but that was nothing compared to the free-kick Drogba curled towards the top corner later on.
Somehow, James managed to reach it. His touch was only faint but it was enough to push the ball onto the bar and down, smack bang onto the goal-line.
So, when Drogba fired a low effort against the post four minutes from half-time, little wonder the offending upright suffered the backlash.
For once, a half had been completed with no one mentioning the pitch.
An odd colour it might have looked but it was not restricting the entertainment value, which included a penalty 10 minutes after the restart.
Introduced for Michael Ballack, who had been the subject of a vicious first-half tackle from Boateng, Juliano Belletti had not quite got his bearings.
And when Dindane nipped past him, the Brazilian lunged in and sent him sprawling.
After all that had gone before, the entire stadium had the sense this was the moment that would give the underdogs the trophy. Except Boateng had not read the script.
So bad was his effort that Cech, having gone down early, had time to make the readjustment required and boot it clear.
Within three minutes, Drogba converted his magnificent free-kick and the dream was over.
Had Lampard scored when he was bundled over in the box by Michael Brown three minutes from time, Chelsea would have deserved it.
He did not. It was that type of extraordinary game.
In the end it didn't matter, The Blues achieving the double for the first, but hopefully not the last, time in their history.