The Germany international's left-footed strike beat Maarten Stekelenburg eight minutes from time after Vlad Chiriches had canceled out Ashkan Dejagah's opener.Lewis Holtby's late goal condemned Fulham to a sixth consecutive defeat in Rene Meulensteen's first match since succeeding Martin Jol.
Having taken over first-team affairs from Jol on Sunday, Meulensteen saw his side turn in an organized display, but it was unable to avoid a loss which leaves it deep in the relegation mire.
Ashkan Dejagah's first Fulham goal looked to have secured the Cottagers a win, but Vlad Chiriches' long-range strike after 73 minutes brought the visitors level.
Substitute Holtby wrapped up the points eight minutes from time with a superb strike from outside the area to end Andre Villas-Boas' side's four-game winless run in the top flight.
Meulensteen made seven changes from Saturday's defeat against West Ham, with Dimitar Berbatov returning from illness.
However, captain Brede Hangeland missed out with a back problem, while there was no place in the squad for Darren Bent.
Villas-Boas made three changes from the Spurs side that drew against Manchester United at White Hart Lane, with Etienne Capoue making his first Premier League start since suffering an ankle injury against Arsenal in September.
Erik Lamela and Jermain Defoe were also brought in, with Nacer Chadli and Roberto Soldado on the bench and Mousa Dembele missing out altogether.
Defoe was the first to threaten for the visitors, stinging the palms of Maarten Stekelenburg with a fierce shot after four minutes, before Berbatov's heavy touch kept him from getting an effort in on goal after a slipped ball from Alexander Kacaniklic.
Berbatov again threatened after 23 minutes, swiveling and firing an effort low to Hugo Lloris' left, with the France international producing a smart save in his 50th Tottenham appearance.
Paulinho weaved through a number of Fulham defenders and should have done better with his finish, firing over the bar from a central position inside the area after good work from Defoe.
Defoe was again the creator after half an hour, laying a ball infield for Lamela who curled just wide of the post.
Pajtim Kasami did well to block Sandro's powerful strike inside the area seven minutes into the second half and Tottenham was made to pay when Dejagah fired past Lloris.
After a lofted ball from Berbatov, the Iranian managed to get the ball under control before finishing well.
The visitors piled on the pressure and were rewarded when Chiriches leveled with an expertly hit half-volley.
Defoe jumped clear of his effort before the ball found its way into the back of the net off Stekelenburg's right-hand post, and Holtby struck to secure the win eight minutes from time.
Berbatov hit the post late for the hosts, but the chances ended there, as Fulham is left with no points from its last possible 18.