But Jol worked his magic when he introduced Kanoute and Keane into the action and was rewarded when both players got their names on the scoresheet.
It was rough justice for Fulham who had defended for their lives throughout the game, but went back to West London empty-handed.
Jol handed a recall to recent signing Mido, who was looking to build on his impressive debut for the club when he netted a brace against Portsmouth.
Andy Reid was also brought back into the starting line-up with Thimothee Atouba being ruled out with a knee injury.
Fulham boss Chris Coleman was boosted by the return of Danish international Claus Jensen, who has missed the majority of the season with a hamstring injury.
But it was the home side who started the strongest and Mido could have made a name for himself once again after just four minutes.
The Egyptian striker made space for himself on the edge of the box, but dragged his shot wide of the post.
Mido, on-loan from AS Roma had two more opportunities to break the deadlock inside the opening 20 minutes.
Simon Davies found the controversial forward completely unmarked inside the box on 11 minutes, but he fired his close-range shot high over the crossbar.
And on 17 minutes, he attempted an ambitious 40-yard lob over Fulham keeper Edwin Van der Sar which went wide of the post.
Tottenham continued to mount pressure on the Fulham goal and Michael Brown came close on 22 minutes when his header inside the box was cleared off the line by Andy Cole.
Coleman's side were hanging on for their lives and had Dutch keeper Van der Sar to thank for keeping them in the game on 27 minutes.
The Fulham defence failed to clear and the ball fell kindly to Reid on the edge of the box who fired a blistering shot which was superbly saved by Van der Sar diving away to his right.
And just two minutes later, Michael Carrick's corner picked out Ledley King whose header was deflected inches past the post.
Fulham had to wait until the 43rd minute before creating their first opportunity of the game.
Papa Bouba Diop found himself completely unmarked inside the Spurs half, but summed up his side's first-half display when he struck his 35-yard drive high over the bar.
Tottenham came close again on 58 minutes when Reid's inswinging corner picked out Noureddine Naybet, but his powerful header flashed just over the bar.
And Davies' goalbound cross caused all kinds of problems for the Fulham defence once again on 71 minutes when Liam Rosenior just managed to turn the ball away for a corner.
The deadlock was finally broken on 77 minutes after Reid had been fouled on the edge of the box by Lee Clark.
Substitute Kanoute made no mistake this time striking a right-foot shot past the stranded Van der Sar into the corner of the net.
And Reid could have made it two for Spurs on 80 minutes when his right-foot shot produced another fantastic save from Van der Sar.
The home side should have sealed all three points on 88 minutes when Kanoute broke free of the Fulham defence and crossed in for Keane, but the Irish international pulled his shot wide.
But he made amends for his error in injury time when he raced on to a high ball over the top of the Fulham defence.
Keane outpaced Luis Boa Morte before taking the ball around the Fulham keeper and sliding the ball into an empty net.
Man of the Match: Mido – The on-loan Egyptian forward caused Fulham all sorts of problems and could have opened the scoring several times before the break.