But the victory came at a cost as Ledley King was injured once again, taken off at half time with an apparent recurrence of his groin injury.
Diomansy Kamara had put Fulham in front on the half-hour mark, but Roman Pavlyuchenko replied instantly in an even game that Fulham will feel unfortunate to have lost.
The winner, on 62 minutes, came when Huddlestone cracked in a long-range cross after a clever corner routine, but William Gallas was standing offside, directly in front of Mark Schwarzer and - while it was inconclusive as to whether he got a touch - the laws of the game state that a player is interfering if he obstructs the view of the goalkeeper, let alone makes a move to play the ball, which Gallas did.
Referee Mike Dean’s decision to allow the goal will be further questioned as it was initially disallowed, with the assistant referee raising his flag: Dean overruled him.
King, whose constant fitness troubles mean he is rarely played more than once a week, was surprisingly named in the starting XI, despite the big Champions League clash against Internazionale looming in midweek.
But he came off just before half-time after twisting awkwardly while attempting a block.
Otherwise it was an impressive performance from both sides, with Spurs making it three wins on the trot since their defeat to West Ham.
An entertaining first half saw Spurs start the better, as Pavlyuchenko fashioned the first opportunity of the game when he drove wide on six minutes.
Fulham initially struggled to get any control of the ball as Spurs had them hemmed into their own half.
But they worked their way back into the match and, by the time Kamara headed just wide from a Simon Davies corner a quarter of an hour in, they were in charge and playing some crisp, passing football.
Aaron Hughes really should have scored when, after a dreadful clearance from Luka Modric, the Northern Ireland defender headed Danny Murphy’s cross over the bar from close range, while Carlos Salcido shaved the outside of the post with a trademark long-range screamer on 28 minutes.
Dean and his assistants were not having the best of games, missing some clear fouls and offsides, and seconds later the Whites had a good penalty appeal waved away when Salcido’s cross clearly struck the arm of Alan Hutton.
It mattered not as, on the half hour, the hosts took a deserved lead when Kamara - who outshone returning strike partner Moussa Dembele in the opening 45 minutes - tapped into an empty net after Clint Dempsey bamboozled King and Gallas with some ball juggling that would not have looked out of place on the beaches of Rio.
Spurs, who were struggling at that point, hit back immediately though, thanks to the fabulous skill of Rafael van der Vaart.
Seconds after the restart, the mercurial Dutchman controlled a high ball with a deft first touch and, from nine yards out, spun 180 degrees before launching an impudent chip over Mark Schwarzer.
It deserved a goal but rattled the crossbar, although Pavlyuchenko was on hand to tap the rebound home from all of a yard.
Both sides went for a second goal, trading attacks until the break, with Fulham going closest when Kamara forced a smart one-handed save from Heurelho Gomes with a rising, first-time shot from the edge of the box.
Gomes’s save was greeted with backslaps but in the aftermath it became apparent that King had picked up yet another an injury while trying to block Kamara’s shot.
Spurs were undeterred though and started the second half well enough.
Aaron Lennon was brought on for Sandro, who was booked as he struggled on his first Premier League start and hauled off at the break, and the England winger immediately had an impact as he found Pavlyuchenko with a far-post cross: Schwarzer was equal to the finish.
Fulham went close when Chris Baird forced another good stop from Gomes, again heading a corner towards goal, while Lennon should have done better for Spurs when he cut inside and fired straight at Schwarzer.
Then came Spurs’ controversial goal which, for all its creativity and technique in execution, should not have stood and, indeed, initially did not.
It took a while for Fulham to recover, but they created a pair of chances that should have drawn them level, Salcido firing over from 12 yards when Gomes dropped a Davies cross, and Kamara doing likewise after Steven Kelly found him unmarked following a superb backheel from Davies.
Spurs had their chances to extend the lead too, with Van der Vaart combining with Gareth Bale and Peter Crouch but the Dutchman’s finish blocked from close range, while Hutton was denied by Schwarzer from the corner that followed.
The final minutes saw Fulham press without really testing the visiting defence, while injury time was owned by Spurs, who just kept it slow and wide in the Fulham half until the whistle.
Fulham slip into the bottom half of the standings after Blackburn and Bolton won.