The former Southampton midfielder helped his side to all three points against Crystal Palace with his first goal for the club.
The Kenyan managed to score a close-range header in the 83rd minute against the Eagles, which was probably deserved on the whole of the game.
Spurs had a number of chances. Harry Kane, Vincent Jannsen and Dele Alli all had chances to score for Tottenham, and Palace 'keeper Wayne Hennessey also made a number of saves to keep his side in the game.
Yohan Cabaye had Palace's best chance of the game, but the Frenchman blazed his shot over the bar from 12 yards.
A draw looked likely until Wanyama managed to score a header from inside six yards in the 83rd minute at White Hart Lane.