The Argentine struck with his fifth goal of the season in all competitions as Mauricio Pochettino's side racked up their fourth straight league win.
Lamela – making his first league start of the campaign – reacted coolly from eight yards out in the 44th minute after he was set up by Moussa Sissoko's elegant cross from the right.
It meant that Tottenham have now made their best start after nine games in the Premier League era.
But West Ham's revival has well and truly crashed as this derby setback followed an away defeat at Brighton.
Manuel Pellegrini's side looked to have recovered from a shocking start when they lost the opening four games.
They won at Everton and then held Chelsea to a goalless draw and beat Manchester United at the London Stadium.
But it was back to a familiar feeling of disappointment for the east London faithful as they faield to hit back despite Marko Arnautovic going close three times early in the second-half.
Hugo Lloris prododiced a superb athletic save to push away Arnautovic's header in the 48th minute following Aaron Cresswell's left-wing cross.
The Austrian forward then produced another good save from Lloris with a low angled shot in the 60th minute.
And he was close once more when he hooked above the bar from the edge of the box five minutes later.
Despite those chances for the home side Tottenham always looked comfortable enough without hitting the top gears.
It was a quiet day for Harry Kane but Sissoko had been close for Tottenham with a 20-yard shot which was deflected above the bar after 10 minutes.
There was a major blow for West Ham when £22 million Ukrainian signing Andriy Yarmalenko was carried off on a stretcher after falling awkwardly while unchallenged in Tottenham's six-yard box in the 43rd minute.
Then there was more misery for the home side when an 85th minute strike by substitute Chicharito was ruled out for offside.
Lloris produced yet more heroics in added time at the end when he dived to block a close range attempt from Arnautovic, who had been fed by Chicharito.
And West Ham were close once more when substitute Michail Antonio thumped a rising drive just over the bar.
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