
Didier Drogba put Chelsea ahead with a free-kick six minutes before half-time but Dimitar Berbatov equalized from the penalty spot (68) and Jonathan Woodgate headed the winner four minutes into the first period of extra time.
The win gave Spurs manager Juande Ramos a trophy just a few months into his reign and also secured European football for next season, with an automatic UEFA Cup spot the reward for the victory.
"I don't normally go for corners, but I just took a chance and put my head on it," an ecstatic Woodgate said.
"I think we were the best team. They were a tough side, but we have done well to come out on top."
Spurs striker Robbie Keane was almost lost for words.
"It's massive, I'm speechless," he said. "This is a dream come true for me. I have dreamt about lifting that Cup. It's unbelievable."
Though Chelsea poured forward in the second period of extra time in search of an equalizer, Tottenham held on, with Paul Robinson, who had been recalled in goal, making a good save to deny substitute Solomon Kalou late on.
Tottenham brought back the fit-again Ledley King to partner Jonathan Woodgate in the centre of defence while Chelsea captain John Terry started, with Frank Lampard restored in midfield, but there was no place in the starting line-up for Michael Ballack or Joe Cole.
Both sides were in action in European competition in midweek, but Spurs, who had a day less to recover, started the stronger, with Robbie Keane forcing a good block from Terry, while Pascal Chimbonda headed onto the crossbar and Berbatov headed wide.
Steed Malbranque forced a good save from Petr Cech but just as Tottenham looked set to take the lead, Chelsea did just that against the run of play. A foul by Didier Zakora gave Chelsea a free-kick on the edge of the box and Drogba fired the ball into the corner, though Robinson's placement left a lot to be desired.
Ramos brought on Tom Huddlestone for Chimbonda early in the second half and the change did the trick as Spurs gradually got back on top.
A difficult ball was allowed to bounce by the Chelsea defence and Wayne Bridge inexplicably handled the ball to give away the penalty. Berbatov coolly sent Cech the wrong way and Spurs were level.
That prompted an onslaught from Tottenham and Zakora should have won with nine minutes to go when he was set clear by Keane, but his shot was blocked by Petr Cech and then he fired the rebound over.
A fantastic turn and shot from Berbatov two minutes later forced another good save from Cech but Chelsea, who brought on Michael Ballack just before the 90 minutes were up, held on for extra time.
Spurs were still the better side as extra time began and from a free-kick on the right, Woodgate outjumped the Chelsea defence to head the ball - with the help of a lucky rbound off his head after Cech tried to block it - into the empty net.
Chelsea finally brought on Joe Cole and as Spurs replaced Keane with Younes Kaboul in a defensive move, Avram Grant's side were invited to attack Spurs.
Cole volleyed a difficult chance over and Kalou almost brought Chelsea level eight minutes from the end but Robinson saved well with his feet.
Tottenham were hanging on at the end, but they kept Chelsea out and their players leapt in delight when the referee finally blew for full time.
By Ben James, dpa