A first-half goal from Didier Drogba, his 10th of the season, put Chelsea on the brink of a second successive Carling Cup triumph but a second-half penalty from Dimitar Berbatov sent the game into extra-time.
Then just four minutes into the extended period, a somewhat fortunate header from Woodgate earned Spurs their first trophy since they claimed the Worthington Cup in 1999.
The pre-match focus had revolved around Chelsea coach Avram Grant's team selection with Frank Lampard and captain John Terry, omitted from the Champions League side against Olympiacos the previous Tuesday, unsure of their places.
But the 52-year-old Israeli, who replaced Jose Mourinho as manager last September, cleverly avoided more controversy by selecting them both in his final line-up.
Instead, it was troubled England left-back Ashley Cole, France veteran Claude Makelele, Germany captain Michael Ballack and England midfielder Joe Cole who found themselves out of luck.
Grant also paired new £15 million signing Nicolas Anelka and Drogba together for the first time in attack but the former was largely anonymous throughout.
The opening half was dominated by Spurs even though they found themselves behind at the interval.
Tottenham's supremacy began from the kick-off when Chelsea full-back Juliano Belletti gave the ball straight to Robbie Keane.
The Irishman couldn't believe his luck but his shot was deflected to safety by Terry - an instant repayment of Grant's faith. In the ninth minute Spurs hit the crossbar when Aaron Lennon's corner was met by the head of Pascal Chimbonda at the far post. Fortunately for Chelsea, the ball dropped onto the top of the bar and out to safety.
Seconds later it was the turn of Berbatov to squander a gilt-edged opportunity when he headed Keane's cross wide of the target from six yards.
Tottenham continued to remain in the ascendancy and in the 27th minute Steed Malbranque brought a fine diving save from Petr Cech when he tried his luck from the edge of the penalty area.
Chelsea, in contrast, had failed to find their normal free-flowing football but Tottenham's inability to find some reward for their control eventually let Grant's side seize back the initiative.
The warning signs were there for Spurs when Didier Zokora brought down Shaun Wright-Phillips on the edge of the penalty area in the 33rd minute.
Drogba's free-kick was a foot wide of the target but when Zokora fouled his Ivory Coast team-mate four minutes later, the misdemeanour had major implications for Juande Ramos' side.
Firstly, Zokora was booked by referee Mark Halsey but the more lethal punishment was to follow.
It arrived a minute later when Drogba's free-kick found the back of the net with the Spurs wall and, more importantly, goalkeeper Paul Robinson completely flat-footed.
Robinson was playing only his second game since being recalled by Ramos following a long spell as number two to Radek Cerny.
Robinson's season has been littered with mistakes and poor judgement both at domestic and international level and his positional questioning was at fault again as Drogba curled his effort into the Spurs net with ease.
Tottenham's response was immediate when Berbatov flicked the ball on to Keane to shoot straight at Cech.
Chelsea continued to look comfortable after the re-start and although Tottenham raised their game it took a fine stop from captain Ledley King to prevent Anelka from increasing their lead in the 65th minute.
But Tottenham found a way back into the game in controversial circumstances in the 69th minute.
Wayne Bridge was adjudged to have handled the ball under pressure from Spurs substitute Tom Huddlestone and the referee's assistant immediately signalled a penalty.
Bulgarian striker Berbatov stepped up to send Cech the wrong way and keep Tottenham's dreams alive.
Spurs were now inspired and they should have gone in front in the 80th minute when Keane sent Zokora clean through with just Cech to beat.
The Chelsea 'keeper saved Zokora's first effort with his face and the Ivory Coast midfielder then blasted the follow-up over the bar.
Grant was clearly concerned by Tottenham's resurgence and he had every right to be especially when Berbatov brought another stunning save from Cech in the 84th minute.
Chelsea were now hanging on like a punch-drunk boxer in the final rounds but Spurs could not find the knockout salvo.
Keane then wasted a chance to win it at the death when a long through ball from Huddlestone was flicked on by Woodgate for the Irishman to hook his shot over the bar.
But Ramos clinched his first trophy as Spurs manager when Anelka fouled Lennon midway in the Chelsea half just four minutes into extra-time.
Woodgate, signed from Middlesbrough in the January transfer window for £8 million, glanced the free-kick from Jermaine Jenas onto Cech's gloves and the ball then rebounded off the Spurs defender's face and into the net.
Robinson justified his selection with seven minutes remaining when he saved superbly to deny Chelsea substitute Salomon Kalou.
Spurs had to withstand some more anxious moments as Chelsea threw everyone forward in an attempt to equalise but the final whistle signalled a fabulous triumph for Ramos who had won his first silverware just four months after taking over from Martin Jol.
Keane said: 'Hopefully this is start of something special, hopefully we can kick on now. It's special for the fans,' he told Sky Sports 1.
'This was a massive test for us and it's unbelievable and a dream come true to come out as winners. I dreamt of this moment as kid and I'm speechless.'
Woodgate said: 'I don't really go up for corners but I took a chance and was able to get my head on it and luckily it went it.
'I think we were the best team and hopefully we can push on from this next year. Chelsea are a top side and they showed that today but we did it.'
Spurs manager Juande Ramos added: 'I am happy because the people (fans) are very happy.'
Spurs defender Ledley King hailed the 'spirit' of his side after they battled back from a goal down to claim the trophy.
'Its amazing. It's been a long time to get here - too long. The only other time we got to a final we lost and we didn't want that to happen today,' King told Sky Sports 1.
'You saw the commitment levels from the players today and we showed we're a good team when we got going today.
'It is tough being 1-0 down. Their goal came from a free-kick but I thought they didn't really create much more than that.
'The spirit was fantastic and at 1-0 down a lot of teams would have folded but we were fantastic to come back and win.
'We have some good players here and hopefully we can use this win and move forward.'
Jermaine Jenas added: 'This is the biggest moment of my career and we've worked so hard for this moment.
'As soon as we got in the changing rooms at half-time we knew we could get back in the game. Then we got that first goal and didn't look back.'
Chelsea boss Avram Grant felt his side were unlucky to lose the match but called on his players to regain focus for the challenges ahead.
'I think even in the second half Tottenham were not in the game and that we were the better side,' Grant said.
'The penalty put them back in the game and that turned the match. The second goal was from a set piece so we are disappointed.
'I did not think it was a penalty. Wayne Bridge could not keep his hand behind his back when he was challenging for the ball and you saw it was not the referee who gave it but the linesman.
'It was always going to be close because cup finals are like this and it was not a great performance from both teams. We tried to score a goal and keep it tight but we lost.'
Grant also admitted he was baffled by referee Mark Halsey's decision to blow the final whistle as Chelsea striker Salomon Kalou broke clear of the Spurs defence in the dying seconds.
'I have never seen such a thing in my life and I have never before seen the referee finish a match when this situation is happening,' Grant added.
'Also in extra time it was not a proper football match with all the stoppages.
'The players are disappointed because we have come a long way to get to the final and we are proud to get here.
'But we still have the Premier League, Champions League and FA Cup so we must now focus on them.'
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