Diomansy Kamara's 90th-minute overhead kick somehow denied us maximum points in Saturday's draw at Craven Cottage.
Gareth Bale looked to have sealed it when he put us 3-1 up just after the hour and we then hit the post through Steed Malbranque, Chris Baird cleared off the line and Antti Niemi made two fine saves to deny Jermaine Jenas and Dimitar Berbatov.
But it all changed with a fortuitous goal back from Alexey Smertin, his 20-yarder looping up and over Paul Robinson via Ricardo Rocha's boot and then as the clock ticked onto 90 minutes, Kamara leaping high to scissor kick home Clint Dempsey's flick-on from Baird's long throw.
You almost had to pinch yourself that it was happening.
A first away win of the season never looked in doubt such was the dominance of the team, who performed with a real zest in their attacking football.
The chances started arriving early in the first half. A corner from the left taken by Keane caused considerable concern in the home rearguard and had Niemi flapping a little and, on ten minutes, one from the other side taken by Bale got the keeper in even more of a pickle. He sought to punch but succeeded only in striking into the back of Ricardo Rocha and the ball ran loose before being tapped into an empty net by Kaboul.
It was his first goal for the Club and a fitting way to mark his return from the hamstring injury he sustained against Everton in our first home game of the season.
Tom Huddlestone and Jermaine Jenas again looked a balanced combination in midfield, with natural width on either side provided by Bale and Steed Malbranque, who was loudly given the bird by his former public.
There was a panic on 19 minutes when a low teasing Hameur Bouazza cross from the left was not completely gathered by Paul Robinson or later dealt with by Kaboul, the Frenchman kicking the ball into Steven Davis leading to it flying over the bar from in front of goal.
The advantage was doubled in an emphatic fashion after 28 minutes when Pascal Chimbonda's throw-in was inadvertently helped on its way to Keane by the head of Davis. Keane struck upwards and onwards into the path of the flying Berbatov, who accelerated past his marker Dejan Stefanovic and slammed past Niemi.
Jenas probably should have made it three moments later only for the Carlos Bocanegra to recover before Keane overdid it with beating defenders in the area and it was Bocanegra to the rescue again.
Fulham, who started the contest brightly enough, were being picked off almost at will with the quality being delivered from central areas
The home side did, however, provide themselves with a lifeline three minutes before the break when a Simon Davies corner was powered home by the head of Clint Dempsey at the near post. The reality is that it should have been game over by this point with the chances created at the other end.
Berbatov was back in the thick of it at the beginning of the second half with a dipping volley from all of 35 yards out that Niemi did not convincingly help over the crossbar.
We were then on the ropes a bit, with Fulham boosted by their pre-break cutting of the deficit. Niemi did have to be sharp to prevent Jenas rattling the net with his rising drive from Keane's knock-down.
It then looked sure to be three when a low cross from Bale was teed up by Keane for Malbranque to have a smash at goal from roughly penalty spot range. Smash the ball he certainly did but, to his disbelief and that of the Spurs thousands behind the goal, his shot cannoned out off the inside of the post.
A richly deserved third came on 61 minutes when, from Kaboul winning a header, Keane provided the touch that set Bale through on goal. The 18-year-old sprinted clear of his marker before calmly slotting past Niemi, low to the goalkeeper's right.
Jenas should then perhaps have added another, but elected to try and cross when the selfish approach might have brought greater profit from well inside the area. A goalbound Berbatov drive was somehow clipped off the line by Chris Baird in the wake of Niemi being stranded after colliding with Bocanegra.
Jermain Defoe was introduced on 68 minutes for Keane, but the next goal was an unlucky one against us as Alexey Smertin took on a shot that hit Ricardo Rocha and looped up over Robinson and landed in the net. Once again it made the game close when it really shouldn't have been.
Fulham took heart and poured forward but Defoe had a chance to seal it, firing over with three minutes left.
There was time for one more attack and it provided a stunning equaliser for Kamara and left us wondering what had hit us.