Aleksandar Kolarov’s own goal and a Dele Alli strike moved Mauricio Pochettino’s men up to second after a 2-0 win at White Hart Lane.
It also left last season’s title challengers as the sole remaining unbeaten side in the top flight.
Wanyama, named Man of the Match, said: “We know we can beat any team. If we continue playing like this it can take us somewhere good, somewhere better than last season.”
Spurs have now conceded just three goals in their seven games so far.
Kenyan midfielder Wanyama added: “We had to make sure that we kept a clean sheet, kept focus.
“It was tough but we always felt that we were strong and we knew we could get something.”
Pochettino said: “I feel very proud. It’s true that we are on a different level to other clubs but we work very hard to try to improve the way we want to play.
“We have enough quality to fight with the big teams. We need to understand we a different project, different team, different club and for that we need to be clever about the way we work.”
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