It also means their boss Juande Ramos has still never lost a cup final as a manager after five triumphs in Spain with Sevilla.
It ends Chelsea's quadruple hopes in Avram Grant's first season as Blues boss, though they are still in the hunt for the Premier League, Champions League and FA Cup.
Spurs set their stall out early on and began in a positive fashion in the first League Cup final at the new Wembley.
With only 30 seconds on the clock Juliano Beletti inexplicably gave the ball away to Robbie Keane, the striker racing through and seeing his 20-yard drive deflected wide by John Terry.
Twice in a minute Spurs could have gone in front, first Chimbonda heading a corner on to the bar and then Berbatov heading wide from Keane's cross, before Chelsea came back into it.
Chelsea's Didier Drogba curls home the opening goal at Wembley
After Frank Lampard shot off target and Drogba curled a 25-yard free-kick high and wide, the Blues made a decisive breakthrough.
Didier Zokora tripped Drogba 20 yards out and the Ivorian dusted himself down to curl the resulting free-kick into the bottom left-hand side of Robinson's goal.
Robinson - only recalled to the Spurs team on Thursday for their Uefa Cup tie after a month on the sidelines - was in completely the wrong position and remained rooted to his spot as the ball flew past him.
Spurs almost made an immediate reply but Keane's shot was straight at Cech and then Berbatov slipped as Keane attempted to send him through on goal.
Chelsea, a side well-drilled in the art of defending a one-goal lead, rarely looked like surrendering their advantage until, halfway through the second half, calamity struck.
Having struggled to make much headway against the Chelsea defence Spurs were gifted a penalty, Bridge bizarrely knocking the ball away with his left hand as he tussled with Aaron Lennon.
Berbatov, keeping his cool, waited for Cech to go left before he rolled the ball into the other side of the goal.
Cech punches the ball against Woodgate and Spurs win the cup
Suddenly Spurs were in the ascendancy and Zokora raced through, only for his first shot to hit Cech on the head and his second slice wide, before Berbatov stung Cech's palms with a fierce drive.
They only had to wait four minutes of extra-time to take a lead they would not relinquish, Cech punching a Jenas free-kick on to Woodgate's head and the ball trickling into an empty net.
Chelsea had to attack but the outstanding Woodgate and Ledley King stood firm, Blues substitute Salomon Kalou and Joe Cole both seeing shots saved by Robinson, but they were nothing more than half-chances.
Spurs deservedly hung on for a famous win and denied their London rivals back-to-back Carling Cup victories in the process.
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