Spurs fielded the side that beat Chelsea in the Carling Cup final - and showed videos of their triumph on the White Hart Lane big screens before kick-off.
The cheers were swiftly silenced as Chelsea swept into a third-minute lead, Drogba heading in John Terry's cross at the far post.
Joe Cole thought he had doubled Chelsea's lead three minutes later when he rounded Spurs keeper Paul Robinson to score, but the strike was ruled out for offside.
Spurs delivered a timely response to level after 12 minutes when Wembley goal hero Woodgate rose above Drogba and Terry to send a powerful header high beyond Carlo Cudicini from Jermaine Jenas's free-kick.
Chelsea looked the more dangerous side and should have restored their lead when Salomon Kalou just failed to apply the finishing touch to Joe Cole's driven cross.
But they did not have long to wait before going back in front, Essien beating Robinson with a neat finish after 20 minutes with the outside of his right foot after a clever ball from Joe Cole unlocked the Spurs defence.
Drogba wasted a good chance to extend Chelsea's advantage two minutes before the break after Frank Lampard robbed Jenas. The striker selfishly shot straight at Robinson with the England midfield man unmarked.
There was an unsavoury scene on the stroke of half-time when Ashley Cole floored Spurs defender Alan Hutton near the touchline with a tackle that was both high and late - and worthy of a red card in the current disciplinary climate.
Chelsea's players - led by England captain John Terry under the watchful eye of coach Fabio Capello - rushed and surrounded referee Mike Riley in a chaotic scene that did them no credit.
When the crowd of Chelsea players finally dispersed, Riley showed leniency in producing only a yellow card - and even then Cole stood pointedly with his back to the official before receiving his punishment.
Joe Cole had been a shining light for Chelsea, and he added a third for Chelsea after 52 minutes when he escaped a flimsy challenge from Pascal Chimbonda to score via Robinson's body.
But Spurs were back in contention after 61 minutes when Berbatov rose above Terry to meet Huddlestone's corner and send a looping header over Cudicini.
The Italian keeper produced a stunning save three minutes later to preserve Chelsea's lead, denying Keane at point-blank range after he was picked out by Berbatov's pass.
It was an end-to-end affair, and Essien almost grabbed his second with a low shot that beat Robinson but rebounded to safety off an upright.
But Spurs' all-out attacking approach paid off with 15 minutes left when Keane's corner fell to the giant Huddlestone, who fired a superb left foot drive beyond Cudicini.
Spurs sensed an unlikely victory, but Chelsea responded in style and the inspirational Joe Cole put them back in front in the 80th minute, shrugging off another weak tackle from Chimbonda to beat Robinson emphatically.
There was another twist after 88 minutes when a long clearance hit Ricardo Carvalho on the back and Keane reacted quickly to curl a 20-yard shot past Cudicini.
And in a grandstand finish, Cudicini produced a wonder save from Berbatov when the Bulgarian looked poised to cap a magnificent match with the winner.
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