Chelsea must have thought they had secured all three points after storming into a 3-1 lead through goals from Didier Drogba, Michael Essien and Joe Cole.
But Tottenham had other ideas and strikes from Dimitar Berbatov and Tom Huddlestone brought Tottenham level.
Avram Grant must still have thought the victory was theirs after Joe Cole added his second of the game to make it 4-3.
But Keane fired an unstoppable shot right at the death to stop Chelsea going level on points with Arsenal in second place.
Chelsea got off to a dream start when Drogba opened the scoring after just three minutes.
Skipper John Terry crossed in for the Ivory Coast striker, who directed his header past Paul Robinson into the corner of the net.
The west London side could have doubled their lead on six minutes but Joe Cole's effort was ruled out for offside against the England midfielder.
Tottenham showed they were up for the fight and grabbed an equaliser on 12 minutes.
Claude Makelele fouled Aaron Lennon on the edge of the box and Jermaine Jenas' free-kick picked out Jonathan Woodgate, who towered above Drogba and headed the ball past Carlo Cudicini.
Chelsea quickly restored their lead when Essien added a second on 20 minutes.
Joe Cole went on a superb run past Didier Zokora to the edge of the box and the ball fell to Essien, who chipped over Robinson to fire Chelsea back into the lead.
The game erupted into controversy on the stroke of half-time after Ashley Cole was allowed to stay on the pitch following a reckless challenge on Alan Hutton.
Referee Mike Riley shocked the home support when he only produced a yellow card to the England defender.
The game looked to be beyond Tottenham when Joe Cole made it three on 52 minutes.
Makelele played the ball through to Cole, who fired his shot through the legs of Robinson into the back of the net.
But despite having nothing to play for in the league, Tottenham showed their fighting spirit when they pulled a goal back on the hour mark.
Huddlestone's corner picked out Berbatov, who rose above Terry to head the ball into the corner.
The Tottenham players could not live with the presence of Joe Cole and he weaved his way past the defence once again before laying the ball into Essien, who saw his shot come back off the post.
Tottenham fans could not believe what they were seeing after Huddlestone brought his team back on level terms on 75 minutes.
Keane's corner fell to the young midfielder, who fired an unstoppable left-foot shot past Cudicini and into the corner of the net.
The game was far from over and Joe Cole thought he had secured all three points for Chelsea when he grabbed his second of the game on 80 minutes.
Drogba played the ball into Cole, who raced past Pascal Chimbonda and struck his shot into the top right-hand corner.
But Tottenham ruined the script when Keane scored the goal of the game on 88 minutes to make it 4-4.
A high ball over the top of the Chelsea defence came back off Ricardo Carvalho's back and Keane was in the right place to curl a spectacular right-foot shot past the stranded Cudicini.
Amazingly, Berbatov could have won the game for Tottenham in injury time but saw his shot superbly saved by the Chelsea keeper.