It was a rather open affair in the first half, however Spurs raced into a two goal lead in the space of three minutes, both from Harry Kane.
Kane, searching for his hat trick, saw his effort from a free kick crash off the bar.
Spurs have won their opening three away league games - the others coming against Newcastle and Everton - and Kane is hoping it continues at Huddersfield next Saturday.
Since losing to Hoffenheim a fortnight ago, Carlo Ancelotti's team had won three games in a row coming into Friday's fixture, but a lacklustre performance underlined its early season problems.
His side needed to draw on all of that team spirit to stand firm when it looked as though they might squander the chance to close the gap on the Premier League leaders.
That's something Spurs are going to have to get used to. There were flashes of real talent against West Ham, but there were also a string of silly fouls in the first half that made a yellow nearly inevitable in the second half.
"I think he was determined to do well after he was sent-off last month and this was a good beginning of the comeback for him, but there is no point or reason to stop, to go "OK, I've done the job".
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Dier has been deployed predominantly in holding midfield this season, but may have found himself in defence more often were it not for a knee injury to Victor Wanyama.
"It happened to us [struggling at home in a new stadium] in the first part of last season".
Slaven Bilic was already in the bad books of the board and supporters after West Ham United finished 11th last season with 45 points. Though Bilic has admitted that Spurs play the most attractive football in the league, he still believes that West Ham can cause an upset.
Dier has never declared his desire to make one role his own but Manchester United expressed an interest in signing him last summer, with the promise of a regular position meant to be tempting.
"And while Spurs have been tenacious in hanging on to star players they have also extracted huge sums in transfers - Gareth Bale's £85million move to Real Madrid was a masterclass in salesmanship by Daniel Levy".
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