Winger Luis Boa Morte fired Fulham ahead on the quarter hour but then saw goalkeeper Maik Taylor dismissed and Teddy Sheringham level from the penalty spot in the 38th minute.
Fulham took the lead against the run of play with 15 minutes gone as Boa Morte pounced on a Steve Marlet flick to scuff a shot home, although a deflection off Ledley King did Spurs no favours.
King nearly made amends on 34 minutes but saw his header draw a world-class save from Taylor in the Fulham goal.
The stand-in shot-stopper then went from hero to villain in the space of four minutes as he appeared to drag down Simon Davies in the box - although television replays showed he got a touch on the ball - and Sheringham made no mistake from the spot against substitute keeper Martin Herrera.
The second half saw Spurs push forward in an attempt to make their numerical advantage count and on 63 minutes Slovenian midfielder Milenko Acimovic should have scored but instead rivalled Ryan Giggs for miss of the season.
Acimovic was just six yards out and needed to slot home but miskicked and the ball hit the crossbar and bounced to safety. It was an unbelievable miss that had the Tottenham fans rubbing their eyes in disbelief.
Just when Spurs looked to be in the driving seat Barber sent Darren Anderton off with 72 minutes gone - the first time in the England man's career - for two bookable offences, although the decision looked a little harsh.
Saha could have won the match shortly afterwards but saw his shot thunder against the crossbar as the match finished all square.
For the match summary click below
Tottenham Hotspur 1 - 1 Fulham
For the Premiership table click here
