He volleyed across Wojciech Szczesny to open the scoring five minutes before half-time.
"To win against Arsenal is great and everyone is so excited, you feel it the whole day and when I scored the first goal again, I was so happy," Van der Vaart told the Spurs website.
"It's crazy. I had a yellow card, so I had to be careful, but you score a goal like that and you forget everything," he said.
"I have to say that how we made the goal was amazing, Jermain did well, a great pass from Adebayor. It was a great goal and I was really happy. It's something special."