Referee Dean allowed Tom Huddlestone's 63rd-minute winner to stand at Craven Cottage after his assistant had initially flagged William Gallas offside.
Fulham had deservedly taken the lead on the half-hour mark when Diomansy Kamara marked his first Premier League start for almost a year with his first goal for the Cottagers in even longer, but Roman Pavlyuchenko levelled almost immediately after brilliant play from Rafael van der Vaart.
However, the match will be remembered for Dean's contentious call and he and his fellow officials left the field to catcalls and chants of: "You don't know what you're doing!"
Spurs, who had come from behind in two of their previous three league games, fielded a strong line-up ahead of Wednesday's Champions League trip to Inter Milan.
The early moments of danger came through Gareth Bale down the left, the winger producing two crosses for lone frontman Pavlyuchenko, the Russian collecting the second and dragging wide from a tight angle.
But it was Fulham who should have taken the lead in the 14th minute when the unmarked Kamara glanced Simon Davies' corner wide.
Tottenham's Sandro had been impressing in central midfield on what was his full Premier League debut but the Brazilian was rightly booked for a second poor tackle in a matter of seconds in the 23rd minute.
And Fulham should have made him pay when Aaron Hughes nodded over from Danny Murphy's right-wing cross.
It was suddenly one-way traffic and Carlos Salcido fired a glorious 25-yard shot just the wrong side of the post.
The home fans screamed for a penalty when the ball appeared to strike the arm of Alan Hutton, and soon afterwards Fulham took the lead half an hour in.
Clint Dempsey was the architect, escaping the attention of surprise starter Ledley King before crossing for the unmarked Kamara to fire home.
But Tottenham levelled from the kick-off, Van der Vaart showing magnificent control in the box and chipping against the crossbar, with Pavlyuchenko converting the rebound.
The half looked set to end level but, less than three minutes before the break, Heurelho Gomes produced a stunning save to tip Kamara's 18-yard half-volley wide.
A minute later, Spurs lost limping captain King, with Sebastien Bassong coming on.
The interval also saw the withdrawal of Sandro, with Aaron Lennon introduced down the right and Luka Modric moved inside.
After the resumption Lennon made almost an immediate impact, his super cross finding Van der Vaart, whose close-range volley was kept out by the foot of Mark Schwarzer.
Fulham captain Murphy - at the centre of a media storm in the build-up to today's game - was replaced seven minutes into the half by Stephen Kelly.
Spurs continued to struggle aerially and Chris Baird forced another acrobatic Gomes save with a header from Davies' corner.
Then came the defining moment of the match, Huddlestone rifling a 25-yard shot through a crowd of players and into the corner of the net.
The fit-again Gallas was in an offside position when the ball was hit and the assistant referee raised his flag.
But after consulting with Dean, the officials appeared to decide Gallas had made no contact and the goal was given.
However, it could be argued the Spurs defender was interfering with play by actively trying to deflect the ball and the Fulham fans were understandably livid.
Van der Vaart then scuffed a volley wide before Pavlyuchenko was replaced by Peter Crouch for the final 20 minutes.
Lennon, who had made a real impact, blazed over from 18 yards and Kamara was close to improvising a flicked finish past Gomes before Mousa Dembele was withdrawn for Zoltan Gera.
Salcido failed to pounce on a collision between Gomes and Hutton when he sliced horribly wide from a difficult angle 11 minutes from time.
But the full-back made some amends moments later with a brilliant challenge to deflect Van der Vaart's close-range finish over.
Schwarzer got fingertips to Hutton's low finish and Crouch was penalised when trying to loop a header over the Fulham goalkeeper.
Kamara blazed over from 15 yards as the end-to-end action continued, with Fulham immediately replacing Jonathan Greening with Eddie Johnson.
The home side poured forward in the closing moments - and Dempsey was booked for dissent - but they were unable to find the goal that would have preserved their unbeaten record.