Referee Mike Dean had reduced Fulham to ten men early in the second half when Heidar Helguson received his second yellow card of the game.
But Fulham thought they had stolen all three points when Michael Dawson gave away a penalty on 82 minutes after the ball appeared to hit his shoulder. Substitute Vincenzo Montella stuck the spot-kick into the corner of the net.
But Chimbonda became an unlikely hero three minutes from time when he popped up in the penalty box to fire the ball past home keeper Jan Lastuvka.
Fulham skipper Michael Brown almost made it a dream start against his former club on eight minutes.
Brown found himself unmarked on the edge of the box and hit a fierce drive which deflected off Chimbonda and flew just wide of the post.
Spurs also came close just sixty seconds later when Jermain Defoe picked out Hossam Ghaly.
Ghaly made a neat turn inside the box but fired his shot straight at Fulham keeper Lastuvka.
Brian McBride then had a golden chance to break the deadlock on ten minutes when he latched on to a through ball by Tomasz Radzinski, but drilled a low shot into the side netting.
Tom Huddlestone, who continues to impress at the heart of the Tottenham midfield, unleashed a blistering 25-yard drive on 19 minutes which sailed inches past the post.
Tottenham continued to mount pressure on the Fulham goal and Anthony Gardner showed his aerial dominance on 27 minutes.
Huddlestone's free-kick picked out the towering defender who rose above the Fulham and flashed a close-range header just over the bar.
Tottenham suffered an injury blow midway through the first half when Finnish international Teemu Tainio was forced to leave the pitch and was replaced by Didier Zokora.
And Fulham almost made them pay sixty seconds later when Carlos Bocanegra picked out McBride who was totally unmarked inside the area.
But with the goal at his mercy the American international tried to be too clever and could only back-heel the ball straight into the path of Paul Robinson in the Tottenham goal.
Robinson showed why he is England's number one keeper when he made a superb save on the stroke of half-time to keep Tottenham in the game.
Franck Queudrue's cross from the left fell to Helguson, whose first-time shot produced a spectacular reflex save from Robinson, who did well to beat the ball away.
Fulham were reduced to ten men on 53 minutes when Helguson received his second yellow card of the game in controversial circumstances.
Helguson made a harmless looking challenge on Huddlestone, but referee Mr Dean was quick to pull out a second yellow card and dismiss the Icelandic striker - much to the disgust of the home supporters.
Dean stole the headlines for all the wrong reasons once again late in the game on 82 minutes when he awarded a penalty to the home side.
McBride's shot appeared to hit Dawson's shoulder, but Dean quickly pointed to the penalty spot.
Substitute Montella made no mistake striking the spot-kick past Robinson into the corner of the net.
But there was to be late drama at Craven Cottage as Chimbonda netted a late equaliser on 87 minutes.
Huddlestone's free-kick fell to the former Wigan defender inside the box and despite getting a hand to the ball, Lastuvka could do nothing to stop the ball crossing the line.