Fulham started the brighter and the threat of Luis Boa Morte down the left proved a thorn in Spurs side for most of the first half.
Once Tottenham had weathered the storm they came closest to breaking the deadlock.
Matt Etherington's cross was missed by Zat Knight who was given a torrid time by the visiting forwards.
Teddy Sheringham slipped the ball wide to Les Fedinand who mis-hit his shot across goal, albeit under pressure from Pierre Wome making his debut.
Simon Davies then issued a warning with his own cross shot which Edwin Van der Sar did well to save low to his right.
There was nothing the giant Dutch keeper could do about the opening goal.
Dean Richards muscled Knight out of the way and met Davies' corner to head the ball into the net from five yards.
After 41 minutes Ethrington stuck out a hopeful leg at the Fulham by line and his cross bounced dangerously across the Fulham goal before Legwinski came to the rescue.
Then with Fulham up against it, Ben Thatcher intercepted a throw-in, headed to Ferdinand, whose lay-off to Etherington allowed him to dribble into the box. His pass was swept majestically into the net by Sheringham from eight yards and Spurs looked out of sight.
Fulham were forced to reorganise after injuries to Luis Saha and Boa Morte and it galvanised their team into a thunderous second-half showing.
Keller was at full stretch to divert a Wome inswinging corner and then again when he flung himself to his right to palm away a right-foot missile from Sean Davis.
But it was the low drive of Junichi Inamoto which kick-started the Fulham comeback. The Japanese midfielder received the ball on the edge of the box and drove low and true into the corner through a posse of players.
The turning point of the game came when Barry Hayles was pulled down just inside the penalty area by Anthony Gardner.
Referee Mark Halsey was having none of the Fulham protests at first, but the resolute flagging of the assistant referee made him change his mind.
Not even a sickening collision which saw Wome crash into Chris Perry could dent the Fulham spirit. Perry was lucky to be able to walk off the pitch but Wome was stretchered off when many thought he should have been sent off.
Steve Finnan could have won it for Fulham when he evaded the Spurs defence but Keller once again saved the day denying the Fulham defender at his feet.
The keeper then parried Malbranque's chance seconds later but could do nothing about the winner from Legwinski which brought a pulsating game to an end.