The home side looked destined to take all three points and climb into the top six in the process when Maik Taylor was sent-off in the 38th minute after bringing down Simon Davies in the area.
Teddy Sheringham stepped up to score from the spot and cancel out Ledley King's 15th minute own goal and it seemed Spurs would go onto push home their advantage.
But a glaring miss by substitute Milenko Acimovic and the 73rd minute dismissal of Darren Anderton left the home side frustrated as they had to settle for a solitary point.
Fulham had been well in control until Taylor was given his marching orders although Sheringham should have given Spurs the lead after only three minutes when he put a free header wide.
That proved costly as Fulham opened the scoring when Steve Marlet played in Luis Boa Morte and the strikers cross cum shot deflected off the unfortunate King and passed a stranded Kasey Keller.
Spurs did their best to get back on level terms and Taylor had to be alert to tip over Anderton's 30-yard screamer and then push King's close ranger header onto the underside of the bar.
However three minutes later Taylor was back in the changing rooms and substitute keeper Martin Herrera's first task was to pick the ball out of the net after Sheringham had beaten him emphatically from the spot.
That should have given Tottenham the encouragement to go on and win the game but the second half proved a frustrating one as Fulham defended in numbers and caught the home side in their off-side trap time after time.
When Spurs did finally break clear Acimovic produced one of the misses of the season. Stephen Carr burst down the right and cut the ball back for the Slovenian six yards out but he caught the ball with his studs and it somehow bounced into the ground and over the bar.
That seemed to take the wind out of Tottenham's sails and their chance of victory diminished even further ten minutes later when Anderton was given his marching orders for a second yellow card.
In fact in the later stages Fulham looked the more likely winners as they counter attacked at pace and they were unlucky not to snatch all three points when Louis Saha crashed a shot against the bar.