The result sees Spurs leapfrog Vitesse in the group with two matches remaining.
Conte received a standing ovation from the Spurs supporters before the game and the Italian couldn't have wished for a better start.
Son put Spurs ahead after 14 minutes with a clinical finish from a tight angle. The South Korea international has now scored the first goal under the Conte, Nuno Espirito Santo and Jose Mourinho eras.
Spurs doubled their lead eight minutes later when Moura was put through from a Harry Kane pass and produced a composed finish.
The hosts grabbed a third after a comical own goal by Rasmussen but the defender immediately made amends with a goal at the other end from a corner.
Bero's fine finish made it 3-2 just before the break, as Spurs lost control of the match.
After 59 minutes, Spurs were reduced to 10 men after Romero received a second yellow card for a cynical challenge.
Spurs goalkeeper Hugo Lloris made a good save to keep Spurs ahead and with 10 minutes to go, the visitors also saw a man sent off after Doekhi brought down Kane on the halfway line.
Moments later, Vitesse were down to nine men after Schubert was adjudged to have handled the ball outside of his area to block Emerson Royal's shot.