Having taken over first-team affairs from Martin Jol on Sunday, Meulensteen saw his side turn in an organised display but they were unable to avoid a sixth successive league defeat.
Ashkan Dejagah's first Fulham goal looked to have secured them a win but Vlad Chiriches' long-range strike after 73 minutes brought the visitors level.
Substitute Lewis 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, 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 put paid to him getting an effort in on goal after a slipped ball from Alexander Kacaniklic.
Berbatov again threatened after 23 minutes, swivelling 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 initially 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 they were made to pay when Dejagah fired past Lloris.
After a lofted ball from Berbatov, Dejagah managed to get the ball under control before finishing well.
The visitors piled on the pressure and were rewarded when Chiriches levelled 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 with Holtby striking in the last 10 minutes.
Berbatov hit the post late on for the hosts but the chances ended there, as Fulham are left with no points from their last possible 18.
