Drogba continued his prolific season with a 20th minute equaliser after Theo Walcott had opened the scoring for a youthful Arsenal with his first goal for the club.
But after Terry had been stretchered off after taking an accidental but heavy blow to the head from the boot of Abou Diaby, Drogba powered home an 84th minute winner to secure more silverware for Jose Mourinho's side.
However, the game ended in controversy as Frank Lampard, Kolo Toure and John Obi Mikel were involved in an ugly spat which ended with three red cards and two yellows - plus both Mourinho and Arsene Wenger both in the centre circle.
Mikel, Toure and substitute Emmanuel Adebayor were given their marching orders by referee Howard Webb as the match descended into an unsavoury end.
It has all started so positively for Arsenal when Walcott fired them into an early lead after beginning and ending a rapier-like move.
The England striker played a neat a one-two with Diaby before picking his spot and scoring with a shot from 12 yards.
Chelsea were chasing shadows at that point but bounced back after slowly feeling their way into the match and Drogba restored parity after 20 minutes.
Michael Ballack chipped an angled ball over the top and Drogba controlled before dispatching a low shot under Manuel Almunia with the Arsenal players appealing for offside.
Petr Cech denied Diaby with a superb 48th minute save and Fabregas drilled an angled effort narrowly wide of the far post.
But Chelsea stepped up a gear and the half-time introduction of Arjen Robben for Claude Makelele had the desired effect.
After a six-minute delay while Terry was tended to on the pitch before being gingerly carried off and going to hospital with a serious head injury, Chelsea responded in positive fashion with an 84th minute winner.
Lampard rattled the crossbar with a 30-yard drive before Mikel intercepted the ball in midfield and fed Robben down the left.
The Dutchman then delivered a pinpoint cross which Drogba powered beyond the diving Almunia after holding off the challenge of Philippe Senderos.
There was still time for the mass brawl to end the match on a sour note, but before the stoppage-time spat, the Millennium Stadium enjoyed a classic match to bring down the curtain on cup finals in Cardiff.