The England Under-21 international moved to White Hart Lane from Sporting Lisbon over the summer and made an instant impact as he grabbed the only goal of the game against Tottenham’s local rivals.
Dier appeared on the edge of the West Ham box in added time to secure three points for the visitors after both teams had been reduced to 10 men.
Kyle Naughton was dismissed for preventing an obvious goalscoring opportunity when he handballed at close range in the first half at the Boleyn Ground, with Mark Noble spurning the chance to score from the resulting penalty, before the Hammers had James Collins sent off after the break.
"I was just really happy to play to be honest and to score on top of that, well, I never imagined it," he said.
"I saw the keeper coming out in the corner of my eye and I wanted to touch the ball around him and put it in. It all happened really quickly. I didn't get any time to think about it and that was probably a good thing."I really enjoyed it and it's why I wanted to come here, to play in games like this. I'm really happy to be here."