Tottenham took the lead on the 25th minute when Pierre-Emile Hojbjerg and Sergio Reguilon set up Harry Kane with a pinpoint cross.
The England international finished the chance with a diving header to put the Londoners ahead.
Tottenham could have doubled their advantage through Son Heung Min but Alphonse Areola stepped up to deny the South Korean.
Fulham were also up to the challenge tonight and the likes of Andre-Frank Zambo Anguissa was denied by Hugo Lloris.
On-loan Chelsea midfielder Ruben Loftus-Cheek came close to scoring for Fulham as well.
Tottenham continued the domination in the second half and Son Heung Min hit the post after being sent clean through on goal on the 71st minute.
Fulham scored the equaliser on the 74th minute after Ademola Lookman managed to find Ivan Cavaleiro in the box with an accurate cross.
Cavaleiro powered in with a bullet header to bring his side level.
Tottenham almost snapped up a late win when Sergio Reguilon managed to score in the final minute of the game but his effort was ruled offside.
Spurs are now up to sixth in the Premier League table with 30 points and Fulham remain in the bottom 3 18th place with just 12 points.
Tottenham will have to improve defensively if they want to secure a top-four finish this season and Fulham need massive improvement to beat the drop.