Dier, a defender who was an offseason signing from Sporting Lisbon, came forward as Tottenham chased a winner and ran on to a through ball from Harry Kane before rounding goalkeeper Adrian and slotting into an empty net in the final moments of the match.
"Andros (Townsend) went outside so I thought I'd make a run inside and it just happened to fall for me,'' Dier said. ``I'd like to score more goals to be honest. We knew it would be a really hard place to come and play. They play really direct football and they played well, but we knew if we stuck in there we might get something and we did that.''
Earlier, Tottenham defender Kyle Naughton was shown a red card in the 29th minute for handball in the area, but West Ham midfielder Mark Noble put the resultant penalty wide.
"I think it was unfair but the more important thing was the team kept calm and never gave up,'' Pochettino said. ``It was a big win and a tough game against West Ham. But this is only the first step. I am happy for the team because we showed the spirit we want to show in every game.''
West Ham center back James Collins was sent off in the second half for a second yellow card after bringing down Emmanuel Adebayor outside the area, before Dier won the match for Tottenham against its London rival.